The Dirichlet problem for the uniformly higher-order elliptic equations in generalized weighted Sobolev-Morrey spaces

TL;DR

This paper establishes a priori estimates for solutions to higher-order elliptic equations with Dirichlet boundary conditions within generalized weighted Sobolev-Morrey spaces, advancing understanding of regularity in complex function spaces.

Contribution

It provides new a priori estimates for weak solutions of higher-order elliptic equations in generalized weighted Sobolev-Morrey spaces, extending previous regularity results.

Findings

A priori estimates for weak solutions are derived.

Results apply to smooth bounded domains in .

Enhances regularity theory in weighted Sobolev-Morrey spaces.

Abstract

A priori estimates for the weak solutions the Dirichlet problem for the uniformly higher-order elliptic equations in a smooth bounded domain $\Omega\subset \Rn$ in generalized weighted Sobolev-Morrey spaces are obtained.