H^s versus C⁰-weighted minimizers

2014/04/24 by Antonio Iannizzotto, Sunra Mosconi, Iannizzotto, Antonio +3 · 1 citation
Computer Science · Mathematics · #35P15 #35P30 #35R11 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1404.6280

openalex publication_date 2014/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C⁰-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.

Citations

• Fractional p-eigenvalues
• The Brezis-Nirenberg result for the fractional Laplacian
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Nonlinear equations for fractional Laplacians I: Regularity, maximum\n principles, and Hamiltonian estimates

Cited by

• Global L^∞ and decay estimate for fractional p-Laplacian equations in D^s,p(\R^N)

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