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arXiv · 2004.03210

Interior Schauder estimates for elliptic equations associated with L\'evy operators

Franziska Kühn
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Abstract

We study the local regularity of solutions $f$ to the integro-differential equation $$ Af=g \quad \text{in $U$}$$ associated with the infinitesimal generator $A$ of a L\'evy process $(X_t)_{t \geq 0}$. Under the assumption that the transition density of $(X_t)_{t \geq 0}$ satisfies a certain gradient estimate, we establish interior Schauder estimates for both pointwise and weak solutions $f$. Our results apply for a wide class of L\'evy generators, including generators of stable L\'evy processes and subordinated Brownian motions.

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Franziska Kühn. 2020-04-07. Interior Schauder estimates for elliptic equations associated with L\'evy operators. https://arxiv.org/abs/2004.03210

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