Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains, Volume 69
1st Edition
Authors:
Michail Borsuk
Vladimir Kondratiev
eBook ISBN: 9780080461731
Hardcover ISBN: 9780444521095
Imprint: Elsevier Science
Published Date: 12th January 2006
Page Count: 538
View all volumes in this series: North-Holland Mathematical Library
Table of Contents
Introduction.
- Preliminaries.
- Integral inequalities.
- The Laplace operator.
- Strong solutions of the Dirichlet problem for linear equations.
- The Dirichlet problem for elliptic linear.
divergent equations in a nonsmooth domain. - The Dirichlet problem for semilinear equations in a conical domain.
- Strong solutions of the Dirichlet problem for nondivergence quasilinear equations.
- Weak solutions of the Dirichlet problem for elliptic divergence form quasilinear equations.
- The behavior of weak solutions to the boundary value problems for elliptic quasilinear equations with triple degeneration in a neighborhood of a boundary edge.
- Sharp estimates of solutions to the Robin.
boundary value problem for elliptic non divergence second order equations in a neighborhood of the conical point.
Bibliography.
Notation Index.
Index.
Description
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.
Key Features
- 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.
Readership
Researchers and graduate students working in the field of partial differential equations.
Details
- No. of pages:
- 538
- Language:
- English
- Copyright:
- © Elsevier Science 2006
- Published:
- 12th January 2006
- Imprint:
- Elsevier Science
- eBook ISBN:
- 9780080461731
- Hardcover ISBN:
- 9780444521095
Ratings and Reviews
About the Authors
Michail Borsuk Author
Affiliations and Expertise
University of Warmia and Mazury in Olsztyn, Poland
Vladimir Kondratiev Author
Affiliations and Expertise
Moscow State University, Russia
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