Lipschitz regularity of almost minimizers in one-phase problems driven by the p-Laplace operator

2022/06/07 by Serena Dipierro, Fausto Ferrari, Dipierro, Serena +5 · 4 citations
Computer Science · Mathematics · #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.03238

openalex publication_date 2022/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that, given~p>max\(2n)/(n+2),1\, the nonnegative almost minimizers of the nonlinear free boundary functional J_p(u,Ω):=∫_Ω( |∇ u(x)|^p+χ_\ugt;0\(x)) dx are Lipschitz continuous.

Cited by

• Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth
• Borderline regularity in singular free boundary problems
• Lipschitz regularity of almost-minimizers in one-phase problems with generalized Orlicz growth
• Lipschitz regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals in Orlicz spaces

Related

• Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot Groups of step two
• Lipschitz regularity of a weakly coupled vectorial almost-minimizers for the p-Laplacian
• Almost minimizers of the one-phase free boundary problem
• Regularity for almost minimizers with free boundary
• Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot groups of step two