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arXiv · 2111.06744

Upper heat kernel estimates for nonlocal operators via Aronson's method

Moritz Kassmann·Marvin Weidner
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Abstract

In his celebrated article, Aronson established Gaussian bounds for the fundamental solution to the Cauchy problem governed by a second order divergence form operator with uniformly elliptic coefficients. We extend Aronson's proof of upper heat kernel estimates to nonlocal operators whose jumping kernel satisfies a pointwise upper bound and whose energy form is coercive. A detailed proof is given in the Euclidean space and extensions to doubling metric measure spaces are discussed.

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Moritz Kassmann, Marvin Weidner. 2021-11-12. Upper heat kernel estimates for nonlocal operators via Aronson's method. https://arxiv.org/abs/2111.06744

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