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Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains
ID: 172021
Michail Borsuk, Vladimir Kondratiev
The book contains a systematic qualification for linear and quasilinear second order equations in non-smooth domains. The authors of the results of the study are the most important ones, as well as regular solutions for solving problems.
Key features:
* New the Hardy - Friedrichs - Wirtinger type inequalities for a differential equation.
* Precise exponents of the solution decreasing near the best possible conditions.
* The question about the impact of 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 the Dirichlet, mixed and the Robin problems.
* The behavior of weak solutions for the Dirichlet problem for m - Laplacian.
* The behavior of weak solutions for elliptic quasilinear equations with triple degeneration.
* Precise exponents of the solution decreasing near the best possible conditions.
* The question about the impact of 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 the Dirichlet, mixed and the Robin problems.
* The behavior of weak solutions for the Dirichlet problem for m - Laplacian.
* The behavior of weak solutions for elliptic quasilinear equations with triple degeneration.
Introduction.
1. Preliminaries.
2. Integral inequalities.
3. The Laplace operator.
4. Strong solutions of the Dirichlet problem for linear equations.
5. The Dirichlet problem for elliptic linear.
divergent equations in a nonsmooth domain.
6. The Dirichlet problem for semilinear equations in a conical domain.
7. Strong solutions of the Dirichlet problem for nondivergence quasilinear equations.
8. Weak solutions of the Dirichlet problem for elliptic divergence form quasilinear equations.
9. The behavior of weaknesses to the limitary value problems for elliptic quasilinear equations with triple degeneration.
10. 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.
172021
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Michail Borsuk, Vladimir Kondratiev