Regularity of radial extremal solutions for some non local semilinear equations

2010/04/12 by Antonio Capella, Capella, Antonio, Juan Dávila +5 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1004.1906

arxiv created 2010/04/12 · arxiv updated 2010/04/13

Abstract

We investigate stable solutions of elliptic equations of the type \ \beginaligned (-Δ)^s u=λf(u) \mbox in B₁ ⊂ \Rⁿ
u= 0 on ∂ B₁,\endaligned . where n≥2, s ∈ (0,1), λ≥ 0 and f is any smooth positive superlinear function. The operator (-Δ)^s stands for the fractional Laplacian, a pseudo-differential operator of order 2s. According to the value of λ, we study the existence and regularity of weak solutions u.

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• Fractional critical systems with mixed boundary conditions
• Edge asymptotics for weighted Robin equations on cylinders with applications to spectral fractional Laplacians

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