Calculus of Variations and Geometric Measure Theory

C. De Filippis - M. Piccinini

Borderline global regularity for nonuniformly elliptic systems

created by piccinini on 16 Jan 2023

[BibTeX]

Published Paper

Inserted: 16 jan 2023
Last Updated: 16 jan 2023

Journal: International Mathematics Research Notices
Year: 2022
Doi: https://doi.org/10.1093/imrn/rnac283

ArXiv: 2206.15330 PDF

Abstract:

We establish sharp global regularity results for solutions to nonhomogeneous, nonunifomrly elliptic systems with zero boundary conditions. In particular, we obtain everywhere Lipschitz continuity under borderline Lorentz assumptions on the forcing term, thus positively settling the optimality issue raised in \cite{bdms}.