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On solutions to "almost everywhere" - Euler-Lagrange equation in Sobolev space $W_2^1$


Abstract

It is known, that if the Euler-Lagrange variational equation is fulfilled everywhere in classical case $C^1$ then it's solution is twice continuously differentiable. The present note is devoted to the study of a similar problem for the Euler-Lagrange equation in the Sobolev space $W_{2}^{1}$.


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Article Information

TitleOn solutions to "almost everywhere" - Euler-Lagrange equation in Sobolev space $W_2^1$
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 3, 262-266
MathSciNet MR2356758
CopyrightThe Author(s) 2007 (CC BY-SA)

Authors Information

E. V. Bozhonok
Mathematics and Computer Science Department, Taurida National V. Vernads'ky University, 4 Vernads'ky Ave., Simferopol', 95007, Ukraine 


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Citation Example

E. V. Bozhonok, On solutions to "almost everywhere" - Euler-Lagrange equation in Sobolev space $W_2^1$, Methods Funct. Anal. Topology 13 (2007), no. 3, 262-266.


BibTex

@article {MFAT408,
    AUTHOR = {Bozhonok, E. V.},
     TITLE = {On solutions to "almost everywhere" - Euler-Lagrange equation in Sobolev space $W_2^1$},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {3},
     PAGES = {262-266},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=408},
}


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