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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 336, Pages 5–24 (Mi znsl194)  
This article is cited in 7 scientific papers (total in 7 papers)

Estimates of the deviation from the minimizer for variational problems with power growth functionals

M. Bildhauera, S. I. Repinb

a Saarland University
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (232 kB) Citations (7)
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Abstract: The paper is concerned with the derivation of directly computable estimates of the difference between approximate solutions and the minimizer of the variational problem
$$ J_\alpha[w]:=\int_\Omega\Big[\frac1\alpha|\nabla w|^\alpha-fw\Big]\,\mathrm dx\to\min. $$
If the functional has a superquadratic growth, then the estimate is given in terms of the natural energy norm. For problems with subquadratic growth it is more convenient to derive such estimates in terms of the dual variational problem. The estimates are obtained for the Dirichlet, Neumann and mixed boundary conditions.
Received: 15.04.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 143, Issue 2, Pages 2845–2856
DOI: https://doi.org/10.1007/s10958-007-0170-x
Bibliographic databases:
UDC: 517
Language: English
Citation: M. Bildhauer, S. I. Repin, “Estimates of the deviation from the minimizer for variational problems with power growth functionals”, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Zap. Nauchn. Sem. POMI, 336, POMI, St. Petersburg, 2006, 5–24; J. Math. Sci. (N. Y.), 143:2 (2007), 2845–2856
Citation in format AMSBIB
\Bibitem{BilRep06}
\by M.~Bildhauer, S.~I.~Repin
\paper Estimates of the deviation from the minimizer for variational problems with power growth functionals
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~37
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 336
\pages 5--24
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl194}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2270877}
\zmath{https://zbmath.org/?q=an:1136.35042}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 2
\pages 2845--2856
\crossref{https://doi.org/10.1007/s10958-007-0170-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247375861}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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