EXISTENCE AND UNIQUENESS OF A SOLUTION TO THE DIRICHLET PROBLEM FOR A QUASILINEAR EQUATION INSIDE AND OUTSIDE A PARABOLOID

摘要

We consider the Dirichlet problem for the equation - div (|▽u|~p-2)▽u) + a|u|~p-2u = 0, where p ∈ (1,∞); a ∈ L∞, a ≥ const > 0, in the exterior, as well as in the interior of an n-dimensional paraboloid, n ≥ 2. We describe boundary traces of functions in the space W_p~1, which implies necessary and sufficient conditions for the existence and uniqueness of a solution. Bibliography. 8 titles.