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