Sobolev versus H "older minimizers for the degenerate fractional\n p-Laplacian

2019/07/20 by Antonio Iannizzotto, Sunra Mosconi, Iannizzotto, Antonio +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1907.08814

Abstract

We consider a nonlinear pseudo-differential equation driven by the fractional\np-Laplacian (-\Δ)^s_p with s\∈(0,1) and p\≥ 2 (degenerate case),\nunder Dirichlet type conditions in a smooth domain \Ω. We prove that\nlocal minimizers of the associated energy functional in the fractional Sobolev\nspace W^s,p₀(\Ω) and in the weighted H "older space\nC⁰_s( Ω), respectively, do coincide.\n

Cited by

• Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces
• Global L^∞ and decay estimate for fractional p-Laplacian equations in D^s,p(\R^N)

Related

• Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case
• Optimization problems in rearrangement classes for fractional p-Laplacian equations
• Minimizing Eigenvalues of the Fractional Laplacian
• Nonlinear equations for fractional Laplacians I: Regularity, maximum\n principles, and Hamiltonian estimates
• Bernoulli problem for the fractional p-Laplacian