Lipschitz regularity of almost-minimizers in one-phase problems with generalized Orlicz growth

2025/08/02 by Chiara Leone, Giovanni Scilla, Leone, Chiara +5
Computer Science · Mathematics · #35J60 #35R35 #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2508.01393

openalex publication_date 2025/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The optimal local Lipschitz regularity for scalar almost-minimizers of Alt-Caffarelli-type functionals F(v; Ω) = ∫_Ωφ(x,|∇ v(x) |)+ λχ_\v gt;0\ (x) dx , with growth function φ a generalized Orlicz function, is established.

Citations

• Lipschitz regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals in Orlicz spaces
• The free boundary for a superlinear system
• Strong existence for free-discontinuity problems with non-standard growth
• Lipschitz regularity of almost minimizers in a Bernoulli problem with non-standard growth
• Almost minimizers for a sublinear system with free boundary
• Lipschitz regularity of almost minimizers in one-phase problems driven by the p-Laplace operator
• Almost minimizers for a singular system with free boundary
• Regularity for almost-minimizers of variable coefficient Bernoulli-type functionals
• Almost minimizers of the one-phase free boundary problem
• Equilibrium points of a singular cooperative system with free boundary
• Regularity for almost minimizers with free boundary
• Regularity of almost minimizers with free boundary
• The φ-harmonic approximation and the regularity of φ-harmonic maps
• A minimum problem with free boundary in Orlicz spaces

Related

• Lipschitz regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals in Orlicz spaces
• Lipschitz regularity of almost minimizers in a Bernoulli problem with non-standard growth
• Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth
• A minimum problem with free boundary and subcritical growth in Orlicz spaces
• Lipschitz regularity of almost minimizers in one-phase problems driven by the p-Laplace operator