Borderline global regularity for nonuniformly elliptic systems

2022/06/30 by De Filippis, Cristiana, Piccinini, Mirco · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.15330

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 \citebdms.

Cited by

• Global Lipschitz regularity in anisotropic elliptic problems with natural gradient growth
• Second-order boundary estimates for solutions to a class of quasilinear elliptic equations

Related

• Regularity theory of elliptic systems in ε-scale flat domains
• Borderline estimates for fully nonlinear elliptic equations
• Regularity of the extremal solutions associated to elliptic systems
• Regularity for solutions of non-uniformly elliptic equations in non-divergence form
• Regularity for nonuniformly elliptic equations with p,q-growth and explicit x,u-dependence