Regularity results via duality for minimizers of degenerate functionals

Article type: Research Article

Authors: Carozza, Menita | Moscariello, Gioconda | Passarelli di Napoli, Antonia^;

Affiliations: Università del Sannio, Piazza Arechi II, Palazzo De Simone, 82100 Benevento, Italy E-mail: [email protected] | Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli “Federico II”, via Cintia, 80126 Napoli, Italy E-mails: {gmoscari; antonia.passarelli}@unina.it

Note: [] Corresponding author.

Abstract: We prove a regularity result for local minimizers of degenerate variational integrals, whose model arises in the study of mappings with finite distortion. The degeneracy function 𝒦(x) lies in the exponential class, i.e., exp (λ𝒦(x)) is integrable for some λ>0. The right space of the gradient of a local minimizer u turns out to be the Zygmund class Lp log −1L. Our result states that if λ is sufficiently large, then Du belongs to the Zygmund space Lp log αL, α≥1 and α increases with λ.

Keywords: degenerate variational integrals, duality theory, mappings with finite distortion

Journal: Asymptotic Analysis, vol. 44, no. 3-4, pp. 221-235, 2005