Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains
- Michail Borsuk, Dr. Sci. in Mathematics, University of Warmia and Mazury in Olsztyn, Poland
- Vladimir Kondratiev, Dr. Sci. in Mathematics, Moscow State University, Russia
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.
* New the Hardy â Friedrichs â 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 â Laplacian.
* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
Researchers and graduate students working in the field of partial differential equations.