Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains
( Volume 69 )
Publication series ：Volume 69
Author： Borsuk Michail;Kondratiev Vladimir
Publisher： Elsevier Science
Publication year： 2006
E-ISBN: 9780080461731
P-ISBN(Paperback): 9780444521095
P-ISBN(Hardback): 9780444521095
Subject： O241 数值分析
Language： ENG
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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.
* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.
* The question about the influence of the co
Chapter