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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 385, Pages 5–17 (Mi znsl3897)  
This article is cited in 6 scientific papers (total in 6 papers)

A geometric maximum principle for variational problems in spaces of vector valued functions of bounded variation

M. Bildhauer, M. Fuchs

Universität des Saarlandes, Fachbereich 6.1 Mathematik, Saarbrücken, Germany
Full-text PDF (192 kB) Citations (6)
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Abstract: We discuss variational integrals with density having linear growth on spaces of vector valued $BV$-functions and prove $\operatorname{Im}(u)\subset K$ for minimizers $u$ provided that the boundary data take their values in the closed convex set $K$ assuming in addition that the integrand satisfies natural structure conditions. Bibl. 14 titles.
Key words and phrases: functions of bounded variation, linear growth problems, minimizers, convex hull property, maximum principle.
Received: 30.05.2010
English version:
Journal of Mathematical Sciences (New York), 2011, Volume 178, Issue 3, Pages 235–242
DOI: https://doi.org/10.1007/s10958-011-0544-y
Bibliographic databases:
Document Type: Article
UDC: 517
Language: English
Citation: M. Bildhauer, M. Fuchs, “A geometric maximum principle for variational problems in spaces of vector valued functions of bounded variation”, Boundary-value problems of mathematical physics and related problems of function theory. Part 41, Zap. Nauchn. Sem. POMI, 385, POMI, St. Petersburg, 2010, 5–17; J. Math. Sci. (N. Y.), 178:3 (2011), 235–242
Citation in format AMSBIB
\Bibitem{BilFuc10}
\by M.~Bildhauer, M.~Fuchs
\paper A geometric maximum principle for variational problems in spaces of vector valued functions of bounded variation
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~41
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 385
\pages 5--17
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3897}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2011
\vol 178
\issue 3
\pages 235--242
\crossref{https://doi.org/10.1007/s10958-011-0544-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80053576815}
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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