Please use this identifier to cite or link to this item:
doi:10.22028/D291-26194
Title: | Partial regularity for a class of anisotropic variational integrals with convex hull property |
Author(s): | Bildhauer, Michael Fuchs, Martin |
Language: | English |
Year of Publication: | 2001 |
Free key words: | anisotropic growth |
DDC notations: | 510 Mathematics |
Publikation type: | Other |
Abstract: | We consider integrands f:\mathbb{R}^{nN}\rightarrow\mathbb{R} which are of lower (upper) growth rate s\geq2(q>s) and which satisfy an additional structural condition implying the convex hull property, i.e. if the boundary data of a minimizer u:\Omega\rightarrow\mathbb{R}^{N} of the energy \int_{\Omega}f(\nabla u)dx respect a closed convex set K\subset\mathbb{R}^{N}, then so does u on the whole domain. We show partial C^{1,\alpha}-regularity of bounded local minimizers if q<min\{s+\frac{2}{3},s\frac{n}{n-2}\} and discuss cases in which the latter condition on the exponents can be improved. Moreover, we give examples of integrands which fit into our category and to which the results of Acerbi and Fusco [AF2] do not apply, in particular, we give some extensions to the subquadratic case. |
Link to this record: | urn:nbn:de:bsz:291-scidok-43579 hdl:20.500.11880/26250 http://dx.doi.org/10.22028/D291-26194 |
Series name: | Preprint / Fachrichtung Mathematik, Universität des Saarlandes |
Series volume: | 38 |
Date of registration: | 25-Nov-2011 |
Faculty: | MI - Fakultät für Mathematik und Informatik |
Department: | MI - Mathematik |
Collections: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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preprint_38_01.pdf | 299,6 kB | Adobe PDF | View/Open |
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