Concentrated reaction terms on the boundary of rough domains for a quasilinear equation

TL;DR

This paper investigates solutions to a p-Laplacian equation with boundary-concentrated nonlinear reactions on rough domains, revealing how boundary oscillations influence the limiting nonlinear boundary conditions.

Contribution

It introduces a new analysis of quasilinear equations with boundary-concentrated reactions on rough domains, deriving the limiting boundary conditions influenced by domain oscillations.

Findings

Derived nonlinear boundary conditions from oscillatory boundary domains.

Analyzed the impact of boundary roughness on solution behavior.

Provided a framework for boundary reactions in quasilinear PDEs.

Abstract

In this work we analyze the solutions of a $p$-Laplacian equation with homogeneous Neumann boundary conditions set in a family of rough domains with a nonlinear term concentrated on the boundary. At the limit, we get a nonlinear boundary condition capturing the oscillatory geometry of the strip where the reactions take place.