Smoothness of generalized solutions for higher-order elliptic equations with nonlocal boundary conditions

TL;DR

This paper investigates the smoothness properties of generalized solutions to higher-order elliptic equations with nonlocal boundary conditions in plane domains, establishing conditions for solution smoothness based on problem data and operators.

Contribution

It provides necessary and sufficient conditions for the smoothness of solutions to complex elliptic problems with nonlocal boundary conditions.

Findings

Identifies conditions under which solutions are smooth

Characterizes the role of nonlocal operators in solution regularity

Establishes criteria linking data and boundary conditions to smoothness

Abstract

Smoothness of generalized solutions for higher-order elliptic equations with nonlocal boundary conditions is studied in plane domains. Necessary and sufficient conditions upon the right-hand side of the problem and nonlocal operators under which the generalized solutions possess an appropriate smoothness are established.