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

2025/05/13 by Matsoukas, Alexandros, Yannakakis, Nikos · 1 citation
#35D30 #35J25 #35J75 Secondary 46E35 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35J60

paper · doi:10.48550/arxiv.2505.08554

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.

Citations

• Euler-Lagrange equations for variable-growth total variation
• Minimizers of abstract generalized Orlicz--bounded variation energy

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• A double-phase Neumann problem with p=1

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