Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

by Michail Borsuk, Vladimir Kondratiev

Series: North-Holland Mathematical Library (Volume 69)

Subject categories
ISBNs
  • 0080461735
  • 9780444521095
  • 9780080461731
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.

  • Elsevier Science; January 2006
  • ISBN: 9780080461731
  • Read online, or download in secure PDF or secure ePub format
  • Title: Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains
  • Series: North-Holland Mathematical Library (Volume 69)
  • Author: Michail Borsuk; Vladimir Kondratiev
  • Imprint: Elsevier Science
Subject categories
ISBNs
  • 0080461735
  • 9780444521095
  • 9780080461731