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Title of Journal: Calc Var

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Abbravation: Calculus of Variations and Partial Differential Equations

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Springer Berlin Heidelberg

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DOI

10.1002/nadc.20164054428

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1432-0835

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Regularity for fully nonlinear nonlocal parabolic

Authors: Joaquim Serra
Publish Date: 2014/11/15
Volume: 54, Issue: 1, Pages: 615-629
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Abstract

We prove space and time regularity for solutions of fully nonlinear parabolic integrodifferential equations with rough kernels We consider parabolic equations u t = mathrmIu where mathrmI is translation invariant and elliptic with respect to the class mathcal L 0sigma of Caffarelli and Silvestre sigma in 02 being the order of mathrmI We prove that if u is a viscosity solution in B 1 times 10 which is merely bounded in mathbb Rn times 10 then u is Cbeta in space and Cbeta /sigma in time in overlineB 1/2 times 1/20 for all beta min sigma 1+alpha where alpha 0 Our proof combines a Liouville type theorem—relaying on the nonlocal parabolic Calpha estimate of Chang and Dávila—and a blow up and compactness argumentThe author is indebted to D Kriventsov X Cabré X RosOton and L Silvestre for their enriching comments on a previous version of this manuscript The author also thanks H ChangLara and the referee for pointing out some typos in the submitted preprint version and for suggesting passages in the proofs that might require a more detailed explanation

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  2. Fractional Poincaré inequality with finite total Q -curvature
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  4. Thick clusters for the radially symmetric nonlinear Schrödinger equation
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  7. Duality for rectified cost functions
  8. An approach to minimization under a constraint: the added mass technique
  9. Single-point condensation phenomena for a four-dimensional biharmonic Ren–Wei problem
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  13. Sharp energy estimates for nonlinear fractional diffusion equations
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  17. Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
  18. Cahn–Hilliard–Navier–Stokes systems with moving contact lines
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