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Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

1st Edition, Volume 69 - January 12, 2006

Authors: Michail Borsuk, Vladimir Kondratiev

Language: English
Hardback ISBN:
9 7 8 - 0 - 4 4 4 - 5 2 1 0 9 - 5
eBook ISBN:
9 7 8 - 0 - 0 8 - 0 4 6 1 7 3 - 1

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… Read more

Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

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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.