The nonlinear Steklov problem in outward cuspidal domains

TL;DR

This paper investigates the nonlinear Steklov eigenvalue problem in outward cuspidal domains, establishing a variational characterization of the first eigenvalue and proving the existence of a weak solution using weighted trace embedding.

Contribution

It introduces a variational approach to the nonlinear Steklov problem in cuspidal domains and proves the existence of solutions, which is a novel contribution.

Findings

First non-trivial eigenvalue characterized variationally

Existence of a weak solution proven

Utilizes weighted trace embedding for analysis

Abstract

In this article, we consider the nonlinear Steklov eigenvalue problem in outward cuspidal domains. Using the compactness of the weighted trace embedding we obtain the variational characterization of the first non-trivial eigenvalue and prove the existence of a corresponding weak solution.