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- Title
Partial regularity for minimizers of a class of non autonomous functionals with nonstandard growth.
- Authors
Giannetti, Flavia; Passarelli di Napoli, Antonia; Ragusa, Maria; Tachikawa, Atsushi
- Abstract
We study the regularity of the local minimizers of non autonomous integral functionals of the type where $$\varPhi $$ is an Orlicz function satisfying both the $$\varDelta _2$$ and the $$\nabla _2$$ conditions, $$p(x):\varOmega \subset {{\mathbb {R}}}^{n}\rightarrow (1,+\infty )$$ is continuous and the function $$A(x,s) = \big (A^{\alpha \beta }_{ij}(x,s)\big )$$ is uniformly continuous. More precisely, under suitable assumptions on the functions $$\varPhi $$ and p( x), we prove the Hölder continuity of the minimizers. Moreover, assuming in addition that the function $$A(x,s) = \big (A^{\alpha \beta }_{ij}(x,s)\big )$$ is Hölder continuous, we prove the partial Hölder continuity of the gradient of the local minimizers too.
- Subjects
INTEGRAL functions; NONSTANDARD mathematical analysis; HARMONIC analysis (Mathematics); LOGARITHMS; SOBOLEV spaces
- Publication
Calculus of Variations & Partial Differential Equations, 2017, Vol 56, Issue 6, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-017-1248-z