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Bibliographic Details
Main Author: Lian, Yuanyuan
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2402.18161
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Table of Contents:
  • We investigate the interior pointwise $C^α$ regularity for weak solutions of elliptic and parabolic equations with divergence-free drifts. For such equations, the integrability condition on the drift can be relaxed and the interior $C^α$ regularity for some $0<α<1$ has been obtained previously with the aid of Harnack inequality. In this paper, we prove the interior pointwise $C^α$ regularity for any $0<α<1$ provided that the drift is small. We obtain the regularity under three different types conditions on the drift. The proof is based on the energy inequality and the perturbation technique.