Well-posedness of fully nonlinear and nonlocal critical parabolic equations

Mathematics – Analysis of PDEs

Scientific paper

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20pages, a maximal principle was added

Scientific paper

In this paper we prove the existence of smooth solutions to fully nonlinear
and nonlocal parabolic equations with critical index. The proof relies on the
apriori H\"older estimate for advection fractional-diffusion equation
established by Silvestre \cite{Si2}.

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