Analysis of a free boundary problem on stratified Lie group

2025/03/03 by Sabri Bensid
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Geometric Analysis and Curvature Flows

paper · doi:10.1016/j.jmaa.2025.129438

Abstract

We present a variational framework for studying the existence of solutions of a class of elliptic free boundary problems on stratified Lie groups . Using the important monotonicity result in a Non-Euclidean setup, we prove that our solution is the limit of mountain pass points of a sequence of C 1 -functionals approximating the energy.

Citations

• Some New Monotonicity Theorems with Applications to Free Boundary Problems
• Variational formulas on Lipschitz domains
• Variational problems with two phases and their free boundaries
• A non-linear eigenvalue problem: The shape at equilibrium of a confined plasma
• Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups
• On semilinear equations with free boundary conditions on stratified Lie groups
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Related

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• On nonminimizing solutions of elliptic free boundary problems