Space-time Hölder continuity with explicit exponents is proved for weak solutions to the parabolic fractional p-Laplacian equation.
Harnack's Inequality for Parabolic Nonlocal Equations
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abstract
The main result of this paper is a nonlocal version of Harnack's inequality for a class of parabolic nonlocal equations. We additionally establish a weak Harnack inequality as well as local boundedness of solutions. None of the results require the solution to be globally positive.
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2019 1verdicts
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Continuity of solutions to a nonlinear fractional diffusion equation
Space-time Hölder continuity with explicit exponents is proved for weak solutions to the parabolic fractional p-Laplacian equation.