English

$ W^{\sigma,p}$ A Priori Estimates for Fully Nonlinear Integro-Differential Equations

Analysis of PDEs 2022-07-15 v1

Abstract

Wσ,pW^{\sigma,p} estimates are studied for a class of fully nonlinear integro-differential equations of order σ\sigma, which are analogues of W2,pW^{2,p} estimates by Caffarelli. We also present Aleksandrov-Bakelman-Pucci maximum principles, which are improvements of estimates proved by Guillen-Schwab, depending only on LpL^p norms of inhomogeneous terms.

Keywords

Cite

@article{arxiv.2207.06728,
  title  = {$ W^{\sigma,p}$ A Priori Estimates for Fully Nonlinear Integro-Differential Equations},
  author = {Shuhei Kitano},
  journal= {arXiv preprint arXiv:2207.06728},
  year   = {2022}
}
R2 v1 2026-06-25T00:54:25.049Z