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arXiv · 1402.5197

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

Ildoo Kim·Kyeong-Hun Kim
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Abstract

We study the integro-differential operators $L$ with kernels $K(y) = a(y) J(y)$, where $J(y)dy$ is a L\'evy measure on $\bR^d$ (i.e. $\int_{\bR^d}(1\wedge |y|^2)J(y)dy<\infty$) 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 $Lu-\lambda u=f$ in $L_p$-spaces and present some $L_p$-estimates of the solutions.

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Ildoo Kim, Kyeong-Hun Kim. 2014-02-21. An L_p-theory for a class of non-local elliptic equations related to nonsymmetric measurable kernels. https://arxiv.org/abs/1402.5197

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