Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution

H. -J. Kim; S. V. Lototsky

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arXiv · 1712.08196

Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution

H. -J. Kim·S. V. Lototsky

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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.

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H. -J. Kim, S. V. Lototsky. 2017-12-21. Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution. https://arxiv.org/abs/1712.08196

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