On existence and uniqueness of variational solutions to Dirichlet boundary value problem for nonlinear elliptic equation with nonstandard growth conditions

Анотація

The Dirichlet boundary value problem for a nonlinear elliptic equation with nonstandard growth conditions in the main part of operator is considered. There is a peculiarity of this problem, which means that without a preliminary definition of an intermediate space, where the solution is searched, a Lavrentiev effect may be observed. Existence and uniqueness of variational solutions for each intermediate weighted Sobolev-Orliсz space are proven.