The one-dimensional nonlocal Dominative $p$-Laplace equation

TL;DR

This paper derives explicit solutions for a class of nonlocal mean value equations on the real line, providing insights into the behavior of solutions to nonlocal elliptic equations.

Contribution

It introduces explicit solutions for a specific nonlocal mean value equation, enhancing understanding of nonlocal elliptic PDEs in one dimension.

Findings

Explicit solutions for the Dirichlet problem are obtained.

The solutions offer insights into the behavior of nonlocal elliptic equations.

The work advances understanding of nonlocal PDEs in one dimension.

Abstract

The explicit solution to the Dirichlet problem for a class of mean value equations on the real line is derived. It shed some light on the behavior of solutions to general nonlocal elliptic equations.