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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 $W_{2}^{1}$.

### Article Information

 Title On solutions to "almost everywhere" - Euler-Lagrange equation in Sobolev space $W_2^1$ Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 3, 262-266 MathSciNet MR2356758 Copyright The 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

### 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},
}