An L_p-theory for a class of non-local elliptic equations related to nonsymmetric measurable kernels

2014/02/21 by Ildoo Kim, Kim, Ildoo, Kyeong-Hun Kim +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1402.5197

arxiv created 2014/02/21 · arxiv updated 2014/02/24

Abstract

We study the integro-differential operators L with kernels K(y) = a(y) J(y), where J(y)dy is a Lévy measure on \bR^d (i.e. ∫_\bR^d(1\wedge |y|²)J(y)dy<∞) and a(y) is an only measurable function with positive lower and upper bounds. Under few additional conditions on J(y), we prove the unique solvability of the equation Lu-λu=f in L_p-spaces and present some L_p-estimates of the solutions.

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