# Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains, Volume 69

## 1st Edition

**Print ISBN:**9780444545992

**eBook ISBN:**9780080461731

**Imprint:**Elsevier Science

**Published Date:**12th January 2006

**Page Count:**538

## 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.

## 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.

## Details

- No. of pages:
- 538

- Language:
- English

- Copyright:
- © Elsevier Science 2006

- Published:
- 12th January 2006

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9780080461731

- Hardcover ISBN:
- 9780444521095

- Paperback ISBN:
- 9780444545992

## Reviews

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.