Global solvability of the Laplace equation in weighted Sobolev spaces

Abstract

We consider a non-local boundary value problem for the Laplace equation in an unbounded strip, studying the weak and strong solvability of the problem within the framework of the weighted Sobolev space W1,pν with a Muckenhoupt weight. Utilising tools from non-harmonic analysis, we prove that any weak solution belonging to W2,pν is also a strong solution and satisfies the corresponding boundary conditions. It is worth noting that such problems do not fall within the scope of the general theory of elliptic equations and therefore require a specialized approach