Heat equation with a geometric rough path potential in one space dimension: existence and regularity of solution
Commun. Korean Math. Soc. 2019 Vol. 34, No. 3, 757-769
https://doi.org/10.4134/CKMS.c180034
Published online July 31, 2019
Hyun-Jung Kim, Sergey V. Lototsky
Illinois Institute of Technology; University of Southern California
Abstract : A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\"{o}lder continuous function, regularity of the resulting solution is in line with the standard parabolic theory.
Keywords : classical solution, fundamental solution, parabolic H\"{o}lder spaces, Stratonovich integral
MSC numbers : Primary 35R05; Secondary 35K20, 35D30, 60H15
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