English

Regularity for fully non linear equations with non local drift

Analysis of PDEs 2012-10-31 v2

Abstract

We prove Holder regularity for solutions of non divergence integro-differential equations with non necessarily even kernels. The even/odd decomposition of the kernel can be understood as a sum of a diffusion and a drift term. In our case we assume that such drift have the order smaller than or equal to the diffusion and at least one. For example we can say something about the following equation Δ1/2u+Du=f\Delta^{1/2}u + |Du| = f. The main step relies in a localized version of the Aleksandrov-Bakelman-Pucci estimate. Our estimates are also uniform as the order of the equation goes to two.

Keywords

Cite

@article{arxiv.1210.4242,
  title  = {Regularity for fully non linear equations with non local drift},
  author = {Hector A. Chang Lara},
  journal= {arXiv preprint arXiv:1210.4242},
  year   = {2012}
}

Comments

Worked on the presentation, corrected some typos and added some figures

R2 v1 2026-06-21T22:22:17.849Z