Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2018.01.30
  • Accepted : 2019.05.28
  • Published : 2019.07.31
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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 $H{\ddot{o}}lder$ continuous function, regularity of the resulting solution is in line with the standard parabolic theory.

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References

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