On the Cauchy problem for integro-differential equations with space-dependent operators in generalized H\"{o}lder classes
Probability
2018-10-04 v2 Analysis of PDEs
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.
Cite
@article{arxiv.1810.00677,
title = {On the Cauchy problem for integro-differential equations with space-dependent operators in generalized H\"{o}lder classes},
author = {Fanhui Xu},
journal= {arXiv preprint arXiv:1810.00677},
year = {2018}
}