-- 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.

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.