Hölder regularity for parabolic fractional p-Laplacian
Naian Liao
Abstract
Abstract Local Hölder regularity is established for certain weak solutions to a class of parabolic fractional p -Laplace equations with merely measurable kernels. The proof uses DeGiorgi’s iteration and refines DiBenedetto’s intrinsic scaling method. The control of a nonlocal integral of solutions in the reduction of oscillation plays a crucial role and entails delicate analysis in this intrinsic scaling scenario. Dispensing with any logarithmic estimate and any comparison principle, the proof is new even for the linear case.
Topics & Concepts
MathematicsLaplace operatorScalingLaplace transformLogarithmMathematical analysisFractional LaplacianClass (philosophy)Oscillation (cell signaling)Hölder conditionPure mathematicsApplied mathematicsGeneticsComputer scienceBiologyArtificial intelligenceGeometryNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNumerical methods in inverse problems