Lipschitz Bounds and Nonuniform Ellipticity

• Published in: Communications on pure and applied mathematics Vol. 73; no. 5; pp. 944 - 1034
• Main Authors: Beck, Lisa, Mingione, Giuseppe
• Format: Journal Article
• Language: English
• Published: Melbourne John Wiley & Sons Australia, Ltd 01.05.2020; John Wiley and Sons, Limited
• Subjects: Ellipticity; Function space; Integrals; Poisson equation; Polynomials; Regularity

We consider nonuniformly elliptic variational problems and give optimal conditions guaranteeing the local Lipschitz regularity of solutions in terms of the regularity of the given data. The analysis catches the main model cases in the literature. Integrals with fast, exponential‐type growth conditio...