On the solutions of a double-phase Dirichlet problem involving the 1-Laplacian

TL;DR

This paper investigates a double-phase Dirichlet problem involving the 1-Laplacian, establishing existence, uniqueness, and a variational characterization of solutions within a suitable weak framework.

Contribution

It introduces a novel approach to solving a double-phase 1-Laplacian problem with non-homogeneous boundary conditions, including a variational formulation.

Findings

Existence of solutions under given conditions

Uniqueness of the solution in a weak sense

Variational characterization of the solution

Abstract

In this paper we study a double-phase problem involving the 1-Laplacian with non-homogeneous Dirichlet boundary conditions and show the existence and uniqueness of a solution in a suitable weak sense. We also provide a variational characterization of this solution via the corresponding minimization problem.