Please use this identifier to cite or link to this item: doi:10.22028/D291-26513
Title: A note on splitting-type variational problems with subquadratic growth
Authors: Breit, Dominic
Language: English
Issue Date: 2009
DDC groups: 510 Mathematics
Publikation type: Preprint
Abstract: We consider variational problems of splitting-type, i.e. we want to minimize \int_{\Omega}\left[f(\tilde{\nabla}w)+g(\partial_{n}w)\right]dx where \tilde{\nabla}=(\partial_{1},...,\partial_{n-1}). Thereby f and g are two C^{2}-functions which satisfy power growth conditions with exponents 1<p\leq q<\infty. In case p\geq2 there is a regularity theory for minimizers u:\mathbb{R}^{n}\supset\Omega\rightarrow\mathbb{R}^{N} without further restrictions on p and q if n = 2 or N = 1. In the subquadratic case the results are much weaker: we get C^{1,\alpha}-regularity, if we require q\leq2p+2 for n = 2 or q < p + 2 for N = 1. In this paper we show C^{1,\alpha}-regularity under the bounds q<\frac{2p+4}{2-p} resp. q<\infty.
URI: urn:nbn:de:bsz:291-scidok-47753
hdl:20.500.11880/26569
http://dx.doi.org/10.22028/D291-26513
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 242
Date issued: 6-Jun-2013
Faculty: MI - Fakultät für Mathematik und Informatik
Institute: MI - Mathematik
Appears in Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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