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Variational problems with obstacles and integral constraints

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Abstract

Various problems in mathematics and physics can be formulated in terms of a variational problem with obstacles and integral constraints, e.g. finding a surface of minimal area with prescribed volume in a bounded region.

We are concerned with the regularity of solutions of variational problems: We show that the minima of a variational integral under all Sobolewfunctions with prescribed boundary values, lying between two obstacles, and fulfilling some integral constraints, are bounded and Hölder-continuous. We do not assume any differentiability or convexity of the integrand, but only a Caratheodory and a growth condition.

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References

  1. Eisen G (1982) Über die Regularität schwacher Lösungen von Variationsproblemen mit Hindernissen und Integralbedingungen. Preprint no. 512, SFB 72, Bonn

  2. Giaquinta M, Giusti E (1981) On the regularity of minima of variational integrals. Preprint no. 429, SFB 72, Bonn

  3. Hildebrandt S, Meier M (1979) On variational problems with obstacles and integral constraints for vector-valued functions. Man Math 28:185–206

    Google Scholar 

  4. Ladyschenskaja O, Uraltsewa N (1968) Linear and Quasilinear Elliptic Equations. Academic Press, New York

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  5. Morrey C (1966) Multiple Integrals in the Calculus of Variations. Springer-Verlag, Berlin-Heidelberg-New York

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Authors and Affiliations

  1. SFB 72, Mathematisches Institut der Universität, Beringstrasse 4, D-5300, Bonn 1, West Germany

    Goswin Eisen

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  1. Goswin Eisen
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Additional information

Communicated by D. Kinderlehrer

This research has been supported by the Sonderforschungsbereich 72 of the Deutsche Forschungsgemeinschaft.

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Eisen, G. Variational problems with obstacles and integral constraints. Appl Math Optim 12, 173–189 (1984). https://doi.org/10.1007/BF01449040

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  • DOI: https://doi.org/10.1007/BF01449040

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