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Lipschitz minimizers for a class of integral functionals under the bounded slope condition.

Lipschitz minimizers for a class of integral functionals under the bounded slope condition.

Authors :
Don, Sebastiano
Lussardi, Luca
Pinamonti, Andrea
Treu, Giulia
Source :
Nonlinear Analysis. Mar2022, Vol. 216, pN.PAG-N.PAG. 1p.
Publication Year :
2022

Abstract

We consider the functional ∫ Ω g (∇ u + X ∗) d L 2 n where g is convex and X ∗ (x , y) = 2 (− y , x) and we study the minimizers in BV (Ω) of the associated Dirichlet problem. We prove that, under the bounded slope condition on the boundary datum, and suitable conditions on g , there exists a unique minimizer which is also Lipschitz continuous. The assumptions on g allow to consider both the case with superlinear growth and the one with linear growth. Moreover neither uniform ellipticity nor smoothness of g are assumed. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
0362546X
Volume :
216
Database :
Academic Search Index
Journal :
Nonlinear Analysis
Publication Type :
Academic Journal
Accession number :
154660768
Full Text :
https://doi.org/10.1016/j.na.2021.112689