Lipschitz regularity for local minimizers of some widely degenerate problems

2014/09/07 by Bousquet, Pierre, Brasco, Lorenzo, Julin, Vesa · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1409.2162

Abstract

We consider local minimizers of the functional ∑_i=1^N ∫ (|u_xi|-δ_i)^p₊ dx+∫ f u dx, where δ₁,…,δ_N≥ 0 and ( ⋅ )₊ stands for the positive part. Under suitable assumptions on f, we prove that local minimizers are Lipschitz continuous functions if N=2 and p≥ 2, or if N≥ 2 and p≥ 4.

Cited by

• Gradient bounds for a widely degenerate orthotropic parabolic equation
• ABP estimate and Harnack inequality for a class of degenerate fully nonlinear pseudo-p-Laplacian equations
• Gradient regularity for double-phase orthotropic functionals

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