Fractional Eigenvalues

2012/03/19 by Lindgren, Erik, Lindqvist, Peter · 7 citations
#35J60 #35P30 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1203.4130

Abstract

We study a non-local eigenvalue problem related to the fractional Sobolev spaces for large values of p and derive the limit equation as p goes to infinity. Its viscosity solutions have many interesting properties and the eigenvalues exhibit a strange behaviour. Keywords: eigenvalue, non-local equation, non-linear equation

Cited by

• An L^∞-variational problem involving the Fractional Laplacian
• Mixed local-nonlocal p-Laplace equation with variable singular nonlinearity in the Heisenberg group
• Nonlocal Harnack inequality in a disconnected region
• Nonlocal singular problem and associated Sobolev type inequality with extremal in the Heisenberg group
• Maz'ya-type bounds for sharp constants in fractional Poincaré-Sobolev inequalities
• Liouville theorem for singular solutions to nonlocal equations
• Global L^∞ and decay estimate for fractional p-Laplacian equations in D^s,p(\R^N)

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