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arXiv · 1810.00677

On the Cauchy problem for integro-differential equations with space-dependent operators in generalized H\"{o}lder classes

Fanhui Xu
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Abstract

Parabolic integro-differential Kolmogorov equations with different space-dependent operators are considered in H\"{o}lder-type spaces defined by a scalable L\'{e}vy measure. Probabilistic representations are used to prove continuity of the operator. Existence and uniqueness of the solution are established and some regularity estimates are obtained.

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Fanhui Xu. 2018-09-27. On the Cauchy problem for integro-differential equations with space-dependent operators in generalized H\"{o}lder classes. https://arxiv.org/abs/1810.00677

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