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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.         
       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 weak solutions to the boundary value problems for elliptic quasilinear equations with triple degeneration in a neighborhood of a boundary edge.
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.
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