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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Minimizers of One-dimensional Parametric Variational Integrals


Author: S. Hildebrandt
Original publication: Algebra i Analiz, tom 27 (2015), nomer 3.
Journal: St. Petersburg Math. J. 27 (2016), 569-576
MSC (2010): Primary 49J05
DOI: https://doi.org/10.1090/spmj/1404
Published electronically: March 30, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: Two different perturbation methods are discussed to establish the existence of normal or quasinormal minimizers for the boundary-value problem of one-dimensional parametric variational problems.


References [Enhancements On Off] (What's this?)

  • 1. G. Buttazzo G., M. Giaquinta, and S. Hildebrandt, One-dimensional variational problems, Oxford Lecture Ser. Math. Appl., vol. 15, Clarendon Press, New York, 1998. MR 1694383
  • 2. U. Dierkes, S. Hildebrandt, and F. Sauvigny, Minimal surfaces, Grundlehren Math. Wiss., Bd. 339, Springer, Berlin, 2010. MR 2566897
  • 3. S. Hildebrandt, H. von der Mosel, Plateau's problem for parametric double integrals. I. Existence and regularity in the interior, Comm. Pure Appl. Math. 56 (2003), no. 7, 926-955. MR 1990482
  • 4. -, Conformal representation of surfaces, and Plateau's problem for Cartan functionals, Riv. Mat. Univ. Parma, (7) 4 (2005), 1-43. MR 2197479

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Additional Information

S. Hildebrandt
Affiliation: Mathematisches Institut, der Universität Bonn Endenicher Allee 60, D-53115 Bonn, Germany
Email: sachinid@math.uni-bonn.de

DOI: https://doi.org/10.1090/spmj/1404
Keywords: Normal and quasinormal minimizers, perturbation methods, parametric variational problems
Received by editor(s): November 10, 2014
Published electronically: March 30, 2016
Dedicated: Dedicated to Nina N. Ural’tseva with great admiration
Article copyright: © Copyright 2016 American Mathematical Society

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