On the Cauchy problem for integro-differential equations with space-dependent operators in generalized Hölder classes

2018/09/27 by Xu, Fanhui
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1810.00677

Abstract

Parabolic integro-differential Kolmogorov equations with different space-dependent operators are considered in Hölder-type spaces defined by a scalable Lévy 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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