Potentials for elliptic boundary value problems in cones

TL;DR

This paper explores solutions to elliptic boundary value problems within conical domains, utilizing wave factorization and boundary conditions to derive explicit formulas, including layer potentials for classical cases.

Contribution

It introduces a wave factorization approach to elliptic problems in cones and provides explicit solution formulas, extending classical layer potential methods.

Findings

Explicit solutions for simple cases are derived.

Wave factorization effectively handles boundary conditions.

The approach generalizes classical layer potential techniques.

Abstract

We consider an elliptic pseudo differential equation in a multi-dimensional cone and starting wave factorization concept we add some boundary conditions. For the simplest cases explicit formulas for solution are given like layer potentials for classical case.