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 atsingular 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.
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