Regularity in the two-phase Bernoulli problem for the p-Laplace operator

2023/01/11 by Bayrami-Aminlouee, Masoud, Fotouhi, Morteza
#35J92 #35R35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.11775

Abstract

We show that any minimizer of the well-known ACF functional (for the p-Laplacian) is a viscosity solution. This allows us to establish a uniform flatness decay at the two-phase free boundary points to improve the flatness, that boils down to C^1,η regularity of the flat part of the free boundary. This result, in turn, is used to prove the Lipschitz regularity of minimizers by a dichotomy argument.

Related

• Regularity of the free boundary for the two-phase Bernoulli problem
• Global minimizers of the two-phase Bernoulli problem with the p-Laplace operator
• Regularity of two-phase free boundary minimizers in periodic media
• Lipschitz regularity of solutions to two-phase free boundary problems
• A two-phase quenching-type problem for the p-Laplacian