Test function approach to fully nonlinear equations in thin domains

TL;DR

This paper extends the test function approach to analyze fully nonlinear equations in thin domains, generalizing previous results that were limited to linear operators like the Laplacian.

Contribution

It introduces a broader framework for handling fully nonlinear operators in thin domain problems, expanding the applicability of existing methods.

Findings

Extended the test function method to fully nonlinear equations in thin domains.

Provided a more general theoretical framework applicable to nonlinear operators.

Enhanced understanding of the behavior of solutions in thin domain settings.

Abstract

In this note we extend to fully nonlinear operators the well known result on thin domains of Hale and Raugel. The result is more general even in the case of the Laplacian.