Krylov D.V.'s Books

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

By: N. V. Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

By: N. V. Krylov

This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

458

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470447401

ISBN 13

9781470447403

Fokker–Planck–Kolmogorov Equations

By: Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Fokker–Planck–Kolmogorov Equations

By: Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

495

Publisher

American Mathematical Society

Published Date

ISBN 10

1470470098

ISBN 13

9781470470098

Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in Cetraro, Italy, August 24 - September 1, 1998

By: N.V. Krylov,M. Röckner,J. Zabczyk

Write a review Read reviews Take a Quiz Solve Book Puzzle

Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions

Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)held in Cetraro, Italy, August 24 - September 1, 1998

By: N.V. Krylov,M. Röckner,J. Zabczyk

Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving existence, uniqueness and regularity results. M. Röckner has presented an approach to Kolmogorov equations in infinite dimensions, based on an LP-analysis of the corresponding diffusion operators with respect to suitably chosen measures. J. Zabczyk started from classical results of L. Gross, on the heat equation in infinite dimension, and discussed some recent results.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

248

Publisher

Springer

Published Date

ISBN 10

3540481613

ISBN 13

9783540481614

Theoretical and Methodical Basics of Investment as a Small and Midsize Business`S Development Tool.

By: Cherep A.V.,Oleinikova L.G.,Cherep O.G.,Krylov D.V.

Write a review Read reviews Take a Quiz Solve Book Puzzle

Theoretical and Methodical Basics of Investment as a Small and Midsize Business`S Development Tool.

By: Cherep A.V.,Oleinikova L.G.,Cherep O.G.,Krylov D.V.

In the monograph theoretical and methodological principles of investment activity and the history of its development have been studied; the investment climate in Ukraine has been focused on; the priority directions of modern governmental investment activities have been determined; the current trends of foreign investments in Ukraine and their interrelations with innovation activity have been analyzed. The concrete proposals for improving the investment climate and the main directions of investment strategy formation in Ukraine have been presented. The role of the state in the investment activity as well as feasibility of state investment policy formation have been determined. The essence and principles of the investment strategy have been investigated. The main tasks of the investment strategy formation have been defined, also promising directions of the investment strategy in Ukraine have been outlined.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

320

Publisher

AuthorHouse

Published Date

ISBN 10

172834316X

ISBN 13

9781728343167

Surface Acoustic Waves in Inhomogeneous Media

By: Sergey V. Biryukov,Yuri V. Gulyaev,Victor V. Krylov,Victor P. Plessky

Write a review Read reviews Take a Quiz Solve Book Puzzle

Surface Acoustic Waves in Inhomogeneous Media

By: Sergey V. Biryukov,Yuri V. Gulyaev,Victor V. Krylov,Victor P. Plessky

Surface Acoustic Waves in Inhomogeneous Media covers almost all important problems of the interaction of different types of surface acoustic waves with surface inhomogeneities. The problems of surface acoustic wave interaction with periodic topographic gratings widely used in filters and resonators are under careful consideration. The most important results of surface wave scattering by local defects such as grooves, random roughness, elastic wedges are given. Different theoretical approaches and practical rules for solving the surface wave problems are presented.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

398

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642577679

ISBN 13

9783642577673

Introduction to the Theory of Random Processes

By: Nikolaĭ Vladimirovich Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Introduction to the Theory of Random Processes

By: Nikolaĭ Vladimirovich Krylov

This book concentrates on some general facts and ideas of the theory of stochastic processes. The topics include the Wiener process, stationary processes, infinitely divisible processes, and Ito stochastic equations. Basics of discrete time martingales are also presented and then used in one way or another throughout the book. Another common feature of the main body of the book is using stochastic integration with respect to random orthogonal measures. In particular, it is used forspectral representation of trajectories of stationary processes and for proving that Gaussian stationary processes with rational spectral densities are components of solutions to stochastic equations. In the case of infinitely divisible processes, stochastic integration allows for obtaining arepresentation of trajectories through jump measures. The Ito stochastic integral is also introduced as a particular case of stochastic integrals with respect to random orthogonal measures. Although it is not possible to cover even a noticeable portion of the topics listed above in a short book, it is hoped that after having followed the material presented here, the reader will have acquired a good understanding of what kind of results are available and what kind of techniques are used toobtain them. With more than 100 problems included, the book can serve as a text for an introductory course on stochastic processes or for independent study. Other works by this author published by the AMS include, Lectures on Elliptic and Parabolic Equations in Holder Spaces and Introduction to the Theoryof Diffusion Processes.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

245

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821829858

ISBN 13

9780821829851

Lectures on Elliptic and Parabolic Equations in Holder Spaces

By: Nikolaĭ Vladimirovich Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures on Elliptic and Parabolic Equations in Holder Spaces

By: Nikolaĭ Vladimirovich Krylov

These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

178

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082180569X

ISBN 13

9780821805695

Works on the Foundations of Statistical Physics

By: Nikolai Sergeevich Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Works on the Foundations of Statistical Physics

By: Nikolai Sergeevich Krylov

Initially published in Moscow in 1950 following the author's death, this book contains the first chapters of a large monograph Krylov planned entitled The foundations of physical statistics," his doctoral thesis on "The processes of relaxation of statistical systems and the criterion of mechanical instability," and a small paper entitled "On the description of exhaustively complete experiments." Originally published in 1980. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

313

Publisher

Princeton University Press

Published Date

ISBN 10

1400854741

ISBN 13

9781400854745

Introduction to Non-Linear Mechanics. (AM-11), Volume 11

By: Nikolai Mitrofanovich Krylov,Nikolai Nikolaevich Bogoliubov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Introduction to Non-Linear Mechanics. (AM-11), Volume 11

By: Nikolai Mitrofanovich Krylov,Nikolai Nikolaevich Bogoliubov

The description for this book, Introduction to Non-Linear Mechanics. (AM-11), Volume 11, will be forthcoming.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

106

Publisher

Princeton University Press

Published Date

ISBN 10

1400882273

ISBN 13

9781400882274

Lectures on Elliptic and Parabolic Equations in Sobolev Spaces

By: Nikolaĭ Vladimirovich Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Lectures on Elliptic and Parabolic Equations in Sobolev Spaces

By: Nikolaĭ Vladimirovich Krylov

This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequesites are basics of measure theory, the theory of $L p$ spaces, and the Fourier transform.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

377

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821846841

ISBN 13

9780821846841

Nonequilibrium Processes in Catalysis

By: Oleg V. Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Nonequilibrium Processes in Catalysis

By: Oleg V. Krylov

Nonequilibrium Processes in Catalysis presents modern ideas and experimental data (e.g., molecular beams, laser technique) on adsorption and catalysis, the mechanism of energy exchange in the processes of particles interaction with a surface, and the lifetimes of excited particles on a surface. Previously unpublished theoretical information regarding the principle of chemoenergetical stimulation accounting for the acceleration of one reaction at the expense of reactant excitation in another is provided, and new ideas about nonequilibrium surface diffusion are explored. Examples of the formation of nonequilibrium dissipative structures in catalysis are presented, including auto-oscillations, auto-waves, multiplicity of kinetic regimes, nonequilibrium phase transition, and decelerated electron exchange between solid and adsorbed species. The book also describes new experimental methods for studying nonequilibrium and quick processes in catalysis. Nonequilibrium Processes in Catalysis will benefit physicists involved with surface science, chemists involved with adsorption and catalysis, engineers, vacuum scientists, physical chemists, materials chemists, students, and others interested in these processes.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

312

Publisher

CRC Press

Published Date

ISBN 10

1351083473

ISBN 13

9781351083478

Approximate Calculation of Integrals

By: V. I. Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Approximate Calculation of Integrals

By: V. I. Krylov

An introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. The 3-part treatment begins with concepts and theorems encountered in the theory of quadrature and then explores the problem of calculation of definite integrals and methods for the calculation of indefinite integral. 1962 edition.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

372

Publisher

Courier Corporation

Published Date

ISBN 10

048615467X

ISBN 13

9780486154671

Industrial Application of Biotechnology

By: Igorʹ Aleksandrovich Krylov,Gennadiĭ Efremovich Zaikov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Industrial Application of Biotechnology

By: Igorʹ Aleksandrovich Krylov,Gennadiĭ Efremovich Zaikov

Industrial Application of Biotechnology

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

152

Publisher

Nova Publishers

Published Date

ISBN 10

1600210392

ISBN 13

9781600210396

Controlled Diffusion Processes

By: N. V. Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Controlled Diffusion Processes

By: N. V. Krylov

Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. ~urin~ that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in Wonham [76]). At the same time, Girsanov [25] and Howard [26] made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4]. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8], Mine and Osaki [55], and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

314

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540709142

ISBN 13

9783540709145

Theoretical and Methodical Basics of Investment as a Small and Midsize Business`S Development Tool.

By: Cherep A.V.,Oleinikova L.G.,Cherep O.G.,Krylov D.V.

Write a review Read reviews Take a Quiz Solve Book Puzzle

Theoretical and Methodical Basics of Investment as a Small and Midsize Business`S Development Tool.

By: Cherep A.V.,Oleinikova L.G.,Cherep O.G.,Krylov D.V.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

320

Publisher

AuthorHouse

Published Date

ISBN 10

172834316X

ISBN 13

9781728343167

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

By: N. V. Krylov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Sobolev and Viscosity Solutions for Fully Nonlinear Elliptic and Parabolic Equations

By: N. V. Krylov

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

458

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470447401

ISBN 13

9781470447403

Fokker-Planck-Kolmogorov Equations

By: Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov

Write a review Read reviews Take a Quiz Solve Book Puzzle

Fokker-Planck-Kolmogorov Equations

By: Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

495

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470425580

ISBN 13

9781470425586

Book's by Krylov D.V.

Username

Password

Password again

Birthday

Email