Dependence Result of the Weak Solution of Robin Boundary Value Problems

TL;DR

This paper establishes how weak solutions to Laplacian problems with Robin boundary conditions depend on the boundary input function, providing an approximation result that clarifies this relationship.

Contribution

It introduces a new approximation result that characterizes the dependence of weak solutions on boundary data for Robin boundary value problems.

Findings

Weak solutions depend continuously on boundary input functions.

The approximation result provides a quantitative measure of this dependence.

The work advances understanding of boundary influence in Robin problems.

Abstract

In this article we establish an approximation result involving the Laplacian with Robin boundary conditions. It informs about the weak solutions dependence from the input function on the boundary.