English

H\"older regularity for parabolic fractional $p$-Laplacian

Analysis of PDEs 2022-05-23 v1

Abstract

Local H\"older regularity is established for certain weak solutions to a class of parabolic fractional pp-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.

Keywords

Cite

@article{arxiv.2205.10111,
  title  = {H\"older regularity for parabolic fractional $p$-Laplacian},
  author = {Naian Liao},
  journal= {arXiv preprint arXiv:2205.10111},
  year   = {2022}
}