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http://dx.doi.org/10.4134/CKMS.c180034

HEAT EQUATION WITH A GEOMETRIC ROUGH PATH POTENTIAL IN ONE SPACE DIMENSION: EXISTENCE AND REGULARITY OF SOLUTION

Kim, Hyun-Jung (Department of Applied Mathematics Illinois Institute of Technology)
Lototsky, Sergey V. (Department of Mathematics University of Southern California)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.3, 2019 , pp. 757-769 More about this Journal

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 $H{\ddot{o}}lder$ continuous function, regularity of the resulting solution is in line with the standard parabolic theory.

Keywords

classical solution; fundamental solution; parabolic $H{\ddot{o}}lder$ spaces; Stratonovich integral;

Citations & Related Records

Reference

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