Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2019; 34(3): 757-769

Online first article July 8, 2019      Printed July 31, 2019

https://doi.org/10.4134/CKMS.c180034

Copyright © The Korean Mathematical Society.

Heat equation with a geometric rough path potential in one space dimension: existence and regularity of solution

Hyun-Jung Kim, Sergey V. Lototsky

Illinois Institute of Technology; University of Southern California

Abstract

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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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