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EnglishWe prove regularity theorems for minimizers of integral functionals of the Calculus of Variations f(x; u;Du) dx; with non-standard growth conditions of (p; q) type |z |p< f(x; z) < L(| z| ^q +1); p < q: In particular,we prove that a sufficient condition for minimizers to be regular is q/p<(n+\alpha)/n ; where the function f(x; z) is Ho lder continuous with respect to the x-variable. This condition is also sharp. We include results in the setting of Orlicz spaces; moreover,we treat certain relaxed functionals too. Finally,we address a problem posed by Marcellini, showing a minimizer with an isolated singularity.
| Titolo: | Sharp regularity for functionals with (q,p) growth |
| Autori: | |
| Data di pubblicazione: | 2004 |
| Rivista: | |
| Abstract: | We prove regularity theorems for minimizers of integral functionals of the Calculus of Variations f(x; u;Du) dx; with non-standard growth conditions of (p; q) type |z |p< f(x; z) < L(| z| ^q +1); p < q: In particular,we prove that a sufficient condition for minimizers to be regular is q/p<(n+\alpha)/n ; where the function f(x; z) is Ho lder continuous with respect to the x-variable. This condition is also sharp. We include results in the setting of Orlicz spaces; moreover,we treat certain relaxed functionals too. Finally,we address a problem posed by Marcellini, showing a minimizer with an isolated singularity. |
| Handle: | http://hdl.handle.net/11386/1188729 |
| Appare nelle tipologie: | 1.1.2 Articolo su rivista con ISSN |
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