Unique continuation for Robin problems with non-smooth potentials

TL;DR

This paper investigates the unique continuation property for Robin boundary value problems with non-smooth potentials, extending previous results to cases where the potential is less regular.

Contribution

It generalizes earlier unique continuation results to Robin problems with potentials in less regular function spaces, broadening the applicability of such properties.

Findings

Established unique continuation for Robin problems with non-smooth potentials

Extended previous results from smooth or zero potentials to less regular cases

Provided new techniques for handling non-smooth boundary potentials

Abstract

In this work, we study the unique continuation properties of Robin boundary value problems with Robin potentials $\eta \in L_{d-1+\varepsilon}$. Our results generalize earlier ones in which $\eta$ was assumed to be either zero (Neumann problem) or differentiable.