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Boundary regularity of minima

Abstract:

Let u: ω → RN be any given solution to the Dirichlet variational problem minw{ωF(x, w, Dw)dx w = u0 on∂ω, where the integrand F(x, w, Dw) is strongly convex in the gradient variable Dw, and suitably Holder continuous with respect to (x, w). We prove that almost every boundary point, in the sense of the usual surface measure of ∂ ω, is a regular point for u. This means that Du is Holder continuous in a relative neighbourhood of the point. The existence of even one such regular boundary point w...

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Publication status:
Published

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Publisher copy:
10.4171/RLM/524

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Mingione, G More by this author
Journal:
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI
Volume:
19
Issue:
4
Pages:
265-277
Publication date:
2008
DOI:
EISSN:
1720-0768
ISSN:
1120-6330
URN:
uuid:d13ad985-031a-4fce-9323-d61008efa033
Source identifiers:
27314
Local pid:
pubs:27314

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