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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.
- 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]
- Subjects :
- *DIRICHLET problem
*FUNCTIONS of bounded variation
*INTEGRALS
*INTEGRAL functions
Subjects
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