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Regularity of ω-minimizers of quasi-convex variational integrals with polynomial growth

✍ Scribed by Frank Duzaar; Manfred Kronz

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
130 KB
Volume
17
Category
Article
ISSN
0926-2245

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✦ Synopsis

We consider almost respectively strong almost minimizers to quasi-convex variational integrals. Under a polynomial growth condition on the integrand and conditions on the function ω determing the almost minimality, in particular the assumption that Ω(r) = r 0 √ ω(ρ)ρ -1 dρ is finite for some r > 0, we establish almost everywhere C 1 -regularity for almost minimizers. Under the weaker assumption that ω is bounded and lim ρ↓0 ω(ρ)=0 we prove almost everywhere C 0,α -regularity for strong almost minimizers to quasi-convex variational integrals of quadratic growth.

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## Abstract If \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$u : {\mathbb R}^{n}\supset \Omega \rightarrow {\mathbb R}^{M} $\end{document} locally minimizes the functional ∫~Ω~__h__(|∇__u__|) __dx__ with __h__ such that ${{h^{\prime }(t)}\over{t}} \le h^{\prime \prime