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.

* 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.