μ-ellipticity and nonautonomous integrals

2025/10/02 by De Filippis, Cristiana
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.02477

Abstract

μ-ellipticity is a form of nonuniform ellipticity arising in various contexts from the calculus of variations. Understanding regularity properties of minimizers in the nonautonomous setting is a challenging task fostering the development of delicate techniques and the discovery of new irregularity phenomena.

Citations

• Bounded minimizers of double phase problems at nearly linear growth
• The sharp growth rate in nonuniformly elliptic Schauder theory
• Scalar minimizers with maximal singular sets and lack of Meyers property
• Quantified Legendreness and the regularity of minima
• Quasiconvex functionals of (p,q)-growth and the partial regularity of relaxed minimizers
• Nonuniformly elliptic Schauder theory
• Regularity for Orlicz phase problems
• Quasiconvexity and partial regularity via nonlinear potentials
• Growth conditions and regularity, an optimal local boundedness result
• New Examples on Lavrentiev Gap Using Fractals
• On the regularity of minima of non-autonomous functionals
• Partial regularity for symmetric quasiconvex functionals on BD
• Higher H "older regularity for the fractional p-Laplacian in the\n superquadratic case
• Regularity for general functionals with double phase
• Regularity for general functionals with double phase
• The Wiener test and potential estimates for quasilinear elliptic equations

Cited by

• Sketches of Nonuniformly Elliptic Schauder Theory

Related

• Nonuniform ellipticity in variational problems and regularity
• On the regularity of minima of non-autonomous functionals
• Modularity over ℂ implies modularity over ℚ
• Integrality properties in the Moduli Space of Elliptic Curves: CM Case
• Quantified Legendreness and the regularity of minima