Global integrability for minimizers of anisotropic functionals

We consider integral functionals in which the density has growth p i with respect to ∂ u ∂ x i , like in ∫ Ω ∂ u ∂ x 1 ( x ) p 1 + ∂ u ∂ x 2 ( x ) p 2 + ⋯ + ∂ u ∂ x n ( x ) p n d x . We show that higher integrability of the boundary datum forces minimizer to be more integrable.

Saved in:
Bibliographic Details
Published inManuscripta mathematica Vol. 144; no. 1-2; pp. 91 - 98
Main Authors Leonetti, Francesco, Siepe, Francesco
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2014
Subjects
Algebraic Geometry
Calculus of Variations and Optimal Control; Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Number Theory
Topological Groups
49N60
35J60
Online AccessGet full text
ISSN0025-2611
1432-1785
DOI10.1007/s00229-013-0641-y

Cover

More Information
Summary:We consider integral functionals in which the density has growth p i with respect to ∂ u ∂ x i , like in ∫ Ω ∂ u ∂ x 1 ( x ) p 1 + ∂ u ∂ x 2 ( x ) p 2 + ⋯ + ∂ u ∂ x n ( x ) p n d x . We show that higher integrability of the boundary datum forces minimizer to be more integrable.
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-013-0641-y