Please use this identifier to cite or link to this item:
doi:10.22028/D291-26298
Title: | Lavrentiev phenomenon, relaxation and some regularity results for anisotropic functionals |
Author(s): | Bildhauer, Michael Fuchs, Martin |
Language: | English |
Year of Publication: | 2004 |
DDC notations: | 510 Mathematics |
Publikation type: | Other |
Abstract: | We study local minimizers of anisotropic variational integrals of the form J[u]=\int_{\Omega}f(\cdot,\nabla u)dx with integrand f satisfying a (p,\bar{q})-growth condition w.r.t. \nabla u and with D_{P}f(x,P) satisfying a Lipschitz condition w.r.t. x\in\Omega. If the Lavrentiev gap functional \mathcal{L} relative to J vanishes for all balls B_{R}\Subset\Omega and if \bar{q}<p(1+1/), then (partial) C^{1,\alpha}-regularity holds. Moreover, the bound on the exponents can be replaced by \bar{q}<p+1 provided we study locally bounded minimizers. We also investigate the relaxation of global minimization problems and discuss the regularity of the corresponding solutions. The importance of the condition \mathcal{L}\equiv0 was recently discovered by Esposito, Leonetti and Mingione in [ELM], where besides other results the higher integrability of the gradient is proved even under weaker assumptions than used here. |
Link to this record: | urn:nbn:de:bsz:291-scidok-44617 hdl:20.500.11880/26354 http://dx.doi.org/10.22028/D291-26298 |
Series name: | Preprint / Fachrichtung Mathematik, Universität des Saarlandes |
Series volume: | 103 |
Date of registration: | 10-Feb-2012 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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