Mikhail Borsuk's Books

Oblique Derivative Problems for Elliptic Equations in Conical Domains

By: Mikhail Borsuk

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Oblique Derivative Problems for Elliptic Equations in Conical Domains

By: Mikhail Borsuk

The aim of our book is the investigation of the behavior of strong and weak solutions to the regular oblique derivative problems for second order elliptic equations, linear and quasi-linear, in the neighborhood of the boundary singularities. The main goal is to establish the precise exponent of the solution decrease rate and under the best possible conditions. The question on the behavior of solutions of elliptic boundary value problems near boundary singularities is of great importance for its many applications, e.g., in hydrodynamics, aerodynamics, fracture mechanics, in the geodesy etc. Only few works are devoted to the regular oblique derivative problems for second order elliptic equations in non-smooth domains. All results are given with complete proofs. The monograph will be of interest to graduate students and specialists in elliptic boundary value problems and their applications.

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Page Count

334

Publisher

Springer Nature

Published Date

ISBN 10

3031283813

ISBN 13

9783031283819

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

By: Mikhail Borsuk

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Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

By: Mikhail Borsuk

This book investigates the behaviour of weak solutions to the elliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges, considering this problem both for linear and quasi-linear equations.

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223

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034604777

ISBN 13

9783034604772

Metric Structures for Riemannian and Non-Riemannian Spaces

By: Mikhail Gromov

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Metric Structures for Riemannian and Non-Riemannian Spaces

By: Mikhail Gromov

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

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Page Count

594

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0817645837

ISBN 13

9780817645830

Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

By: Mikhail I. Kamenskii,Valeri V. Obukhovskii,Pietro Zecca

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Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

By: Mikhail I. Kamenskii,Valeri V. Obukhovskii,Pietro Zecca

The theory of set-valued maps and of differential inclusion is developed in recent years both as a field of his own and as an approach to control theory. The book deals with the theory of semilinear differential inclusions in infinite dimensional spaces. In this setting, problems of interest to applications do not suppose neither convexity of the map or compactness of the multi-operators. These assumption implies the development of the theory of measure of noncompactness and the construction of a degree theory for condensing mapping. Of particular interest is the approach to the case when the linear part is a generator of a condensing, strongly continuous semigroup. In this context, the existence of solutions for the Cauchy and periodic problems are proved as well as the topological properties of the solution sets. Examples of applications to the control of transmission line and to hybrid systems are presented.

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Page Count

245

Publisher

Walter de Gruyter

Published Date

ISBN 10

3110870894

ISBN 13

9783110870893

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

By: Mikhail Borsuk

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Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

By: Mikhail Borsuk

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Page Count

223

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3034604777

ISBN 13

9783034604772

Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

By: Michail Borsuk,Vladimir Kondratiev

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Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

By: Michail Borsuk,Vladimir Kondratiev

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.Key features:* New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

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Page Count

538

Publisher

Elsevier

Published Date

ISBN 10

0080461735

ISBN 13

9780080461731

Book's by Mikhail Borsuk

Oblique Derivative Problems for Elliptic Equations in Conical Domains

Oblique Derivative Problems for Elliptic Equations in Conical Domains

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

Metric Structures for Riemannian and Non-Riemannian Spaces

Metric Structures for Riemannian and Non-Riemannian Spaces

Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

Transmission Problems for Elliptic Second-Order Equations in Non-Smooth Domains

Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

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