Nonuniform ellipticity in variational problems and regularity

2025/09/17 by De Filippis, Cristiana, Mingione, Giuseppe · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.14114

Abstract

We provide a brief outlook on recent developments in regularity theory for nonuniformly elliptic problems, with special emphasis on those of variational nature.

Citations

• The sharp growth rate in nonuniformly elliptic Schauder theory
• Quantified Legendreness and the regularity of minima
• Quasiconvex functionals of (p,q)-growth and the partial regularity of relaxed minimizers
• Nonuniformly elliptic Schauder theory
• Quasiconvexity and partial regularity via nonlinear potentials
• The Wiener test and potential estimates for quasilinear elliptic equations

Cited by

• Global boundedness of weak solutions with finite energy to a general class of Dirichlet problems
• Regularity for quasilinear elliptic equations in metric measure spaces
• Sketches of Nonuniformly Elliptic Schauder Theory

Related

• Nonlinear potential theoretic methods in nonuniformly ellliptic problems
• μ-ellipticity and nonautonomous integrals
• Quantified Legendreness and the regularity of minima
• Regularity for nonuniformly elliptic equations with p,q-growth and explicit x,u-dependence
• Note on Regularity theory for Nonlinear elliptic equations