On Some Elliptic Interface Problems with Nonhomogeneous Jump Conditions

TL;DR

This paper investigates elliptic interface problems with nonhomogeneous jump conditions, providing solutions relevant to chemical reactions and inclusions, using Morse theory and concentration compactness methods.

Contribution

It introduces new solution existence results for elliptic interface problems with nonhomogeneous jumps, employing Morse theory and concentration compactness techniques.

Findings

Existence of nontrivial solutions established

Application to chemical reaction models demonstrated

Extension of methods to unbounded domains achieved

Abstract

We obtain nontrivial solutions of some elliptic interface problems with nonhomogeneous jump conditions that arise in localized chemical reactions and nonlinear neutral inclusions. Our proofs in bounded domains use Morse theoretical arguments, in particular, critical group computations. An extension to the whole space is proved using concentration compactness arguments.