Borderline regularity for fully nonlinear equations in Dini domains
Abstract
In this paper, we prove borderline gradient continuity of viscosity solutions to Fully nonlinear elliptic equations at the boundary of a $C^{1,\dini}$-domain. Our main result Theorem 3.1 is a sharpening of the boundary gradient estimate proved by Ma-Wang following the borderline interior gradient regularity estimates established Daskalopoulos-Kuusi-Mingione. We however mention that, differently from the approach in the interior case which depends on $W^{1,q}$ estimates, our proof is slightly more geometric and is based on compactness arguments inspired by the techniques in the fundamental works of Caffarelli.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2018
- DOI:
- 10.48550/arXiv.1806.07652
- arXiv:
- arXiv:1806.07652
- Bibcode:
- 2018arXiv180607652A
- Keywords:
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- Mathematics - Analysis of PDEs
- E-Print:
- a few typos corrected