Abstract
AbstractIn 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.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
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