On semilinear equations with free boundary conditions on stratified Lie groups

2022/09/13 by Debajyoti Choudhuri, Dušan D. Repovš, Dušan Repovš · 2 citations
Mathematics · Computer Science · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering

paper · doi:10.1016/j.jmaa.2022.126677

Abstract

In this paper we establish existence of a solution to a semilinear equation with free boundary conditions on stratified Lie groups. In the process, a monotonicity condition is proved, which is quintessential in establishing the regularity of the solution.

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
• Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

Cited by

• Analysis of a free boundary problem on stratified Lie group
• Quasilinear equations with exponential growth for Hörmander q-sub-Laplacians on stratified Lie groups

Related

• Analysis of a free boundary problem on stratified Lie group
• Analysis of a free boundary problem on stratified Lie group
• Boundary behavior of positive solutions of the heat equation on a stratified Lie group
• A molecular method applied to a non-local PDE in stratified Lie groups
• Local and Global Analysis of Semilinear Heat Equations with Hardy Potential on Stratified Lie Groups