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2011

On $L_p$-estimates for a class of non-local elliptic equations

Dong, Hongjie, Kim, Doyoon

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We consider non-local elliptic operators with kernel $K(y)=a(y)/|y|^{d+\sigma}$, where $0 < \sigma < 2$ is a constant and $a$ is a bounded measurable function.

By using a purely analytic method, we prove the continuity of the non-local operator $L$ from the Bessel potential space $H^\sigma_p$ to $L_p$, and the unique strong solvability of the corresponding non-local elliptic equations in $L_p$ spaces.
As a byproduct, we also obtain interior $L_p$-estimates.
The novelty of our results is that the function $a$ is not necessarily to be homogeneous, regular, or symmetric.

On $L_p$-estimates for a class of non-local elliptic equations · Around

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