Well-posedness of fully nonlinear and nonlocal critical parabolic equations

Abstract

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 Hölder estimate for advection fractional-diffusion equation established by Silvestre \cite{Si2}.

20pages, a maximal principle was added

References in corpus (2)

• $L^p$-maximal regularity of nonlocal parabolic equation and applications
• Regularity for solutions of non local parabolic equations

Cited by in corpus (2)

• Heat kernel estimates for critical fractional diffusion operator
• $L^p$-solvability of nonlocal parabolic equations with spatial dependent and non-smooth kernelsXiche