Enrico Magenes's Books

Non-Homogeneous Boundary Value Problems and Applications

Volume II

By: Jacques Louis Lions,Enrico Magenes

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Non-Homogeneous Boundary Value Problems and Applications

Volume II

By: Jacques Louis Lions,Enrico Magenes

I. In this second volume, we continue at first the study of non homogeneous boundary value problems for particular classes of evolu tion equations. 1 In Chapter 4 , we study parabolic operators by the method of Agranovitch-Vishik [lJ; this is step (i) (Introduction to Volume I, Section 4), i.e. the study of regularity. The next steps: (ii) transposition, (iii) interpolation, are similar in principle to those of Chapter 2, but involve rather considerable additional technical difficulties. In Chapter 5, we study hyperbolic operators or operators well defined in thesense of Petrowski or Schroedinger. Our regularity results (step (i)) seem to be new. Steps (ii) and (iii) are all3.logous to those of the parabolic case, except for certain technical differences. In Chapter 6, the results of Chapter'> 4 and 5 are applied to the study of optimal control problems for systems governed by evolution equations, when the control appears in the boundary conditions (so that non-homogeneous boundary value problems are the basic tool of this theory). Another type of application, to the characterization of "all" well-posed problems for the operators in question, is given in the Ap pendix. Still other applications, for example to numerical analysis, will be given in Volume 3.

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Page Count

255

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642652174

ISBN 13

9783642652172

Geometry of Algebraic Curves

Volume I

By: Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths,Joseph Daniel Harris

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Geometry of Algebraic Curves

Volume I

By: Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths,Joseph Daniel Harris

In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves).

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Page Count

402

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475753233

ISBN 13

9781475753233

Direct Methods In The Calculus Of Variations

By: Enrico Giusti

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Direct Methods In The Calculus Of Variations

By: Enrico Giusti

This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.

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Page Count

412

Publisher

World Scientific

Published Date

ISBN 10

9814488291

ISBN 13

9789814488297

Applied and Industrial Mathematics in Italy III

By: Enrico De Bernardis

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Applied and Industrial Mathematics in Italy III

By: Enrico De Bernardis

This book provides an up-to-date overview of research articles in applied and industrial mathematics in Italy. This is done through the presentation of a number of investigations focusing on subjects as nonlinear optimization, life science, semiconductor industry, cultural heritage, scientific computing and others. This volume is important as it gives a report on modern applied and industrial mathematics, and will be of specific interest to the community of applied mathematicians. This book collects selected papers presented at the 9th Conference of SIMAI. The subjects discussed include image analysis methods, optimization problems, mathematics in the life sciences, differential models in applied mathematics, inverse problems, complex systems, innovative numerical methods and others. Sample Chapter(s). Chapter 1: Multichannel Wavelet Scheme for Color Image Processing (759 KB). Contents: Existence and Uniqueness for a Three Dimensional Model of Ferromagnetism (V Berti et al.); Wave Propagation in Continuously-Layered Electromagnetic Media (G Caviglia & A Morro); Mathematical Models for Biofilms on the Surface of Monuments (F Clarelli et al.); Conservation Laws with Unilateral Constraints in Traffic Modeling (R M Colombo et al.); On a Model for the Codiffusion of Isotopes (E Comparini et al.); Multiscale Models of Drug Delivery by Thin Implantable Devices (C D''Angelo & P Zunino); A Mathematical Model of Duchenne Muscular Dystrophy (G Dell''Acqua & F Castiglione); A Dissipative System Arising in Strain-Gradient Plasticity (L Giacomelli & G Tomassetti); Material Symmetry and Invariants for a 2D Fiber-Reinforced Network with Bending Stiffness (G Indelicato); Kinetic Treatment of Charge Carrier and Phonon Transport in Graphene (P Lichtenberger et al.); Mathematical Models and Numerical Simulation of Controlled Drug Release (S Minisini & L Formaggia); A Lattice Boltzmann Model on Unstructured Grids with Application in Hemodynamics (G Pontrelli et al.); Toward Analytical Contour Dynamics (G Riccardi & D Durante); Thermo-Mechanical Modeling of Ground Deformation in Volcanic Areas (D Scandura et al.); and other papers. Readership: Researchers in applied and computational mathematics.

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Page Count

590

Publisher

World Scientific

Published Date

ISBN 10

9814280305

ISBN 13

9789814280303

Non-Homogeneous Boundary Value Problems and Applications

Volume III

By: Jacques Louis Lions,Enrico Magenes

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Non-Homogeneous Boundary Value Problems and Applications

Volume III

By: Jacques Louis Lions,Enrico Magenes

1. Our essential objective is the study of the linear, non-homogeneous problems: (1) Pu = I in CD, an open set in RN, (2) fQjtl = gj on am (boundary of m), lor on a subset of the boundm"J am 1

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Page Count

323

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642653936

ISBN 13

9783642653933

Non-Homogeneous Boundary Value Problems and Applications

Volume II

By: Jacques Louis Lions,Enrico Magenes

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Non-Homogeneous Boundary Value Problems and Applications

Volume II

By: Jacques Louis Lions,Enrico Magenes

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Page Count

255

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642652174

ISBN 13

9783642652172

Non-Homogeneous Boundary Value Problems and Applications

Vol. 1

By: Jacques Louis Lions,Enrico Magenes

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Non-Homogeneous Boundary Value Problems and Applications

Vol. 1

By: Jacques Louis Lions,Enrico Magenes

1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and Qj' 0 ~ i ~ 'V. By "non-homogeneous boundary value problem" we mean a problem of the following type: let f and gj' 0 ~ i ~ 'v, be given in function space s F and G , F being a space" on m" and the G/ s spaces" on am" ; j we seek u in a function space u/t "on m" satisfying (1) Pu = f in m, (2) Qju = gj on am, 0 ~ i ~ 'v«])). Qj may be identically zero on part of am, so that the number of boundary conditions may depend on the part of am considered 2. We take as "working hypothesis" that, for fEF and gjEG , j the problem (1), (2) admits a unique solution u E U/t, which depends 3 continuously on the data . But for alllinear probIems, there is a large number of choiees for the space s u/t and {F; G} (naturally linke d together). j Generally speaking, our aim is to determine families of spaces 'ft and {F; G}, associated in a "natural" way with problem (1), (2) and con j venient for applications, and also all possible choiees for u/t and {F; G} j in these families.

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Page Count

375

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642651615

ISBN 13

9783642651618

Book's by Enrico Magenes

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

Geometry of Algebraic Curves

Geometry of Algebraic Curves

Direct Methods In The Calculus Of Variations

Direct Methods In The Calculus Of Variations

Applied and Industrial Mathematics in Italy III

Applied and Industrial Mathematics in Italy III

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

Non-Homogeneous Boundary Value Problems and Applications

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