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ArticleOriginal scientific text

Title

The generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order

Authors 1

Affiliations

  1. Institute of Mathematics, Łódź University, Stefana Banacha 22, 90-238 Łódź, Poland

Abstract

In the paper, the generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order is proved. Some application of this theorem to the coercive Dirichlet problem is given.

Bibliography

  1. D. Idczak and S. Walczak, On the existence of a solution for some distributed optimal control hyperbolic system, to appear in International Journal of Mathematics and Mathematical Sciences, University of Central Florida.
  2. L. A. Lusternik and W. I. Sobolew, Elements of Functional Analysis, Warsaw 1959, (Polish).
  3. J. Mawhin, Problèmes de Dirichlet Variationnels Non-Linéaires, L'Université de Montréal, 1987.
  4. S. Walczak, On some generalization of the fundamental lemma and its application to differential equations, Bull. Soc. Math. Belg. 45(3) ser. B (1993).
  5. S. Walczak, On the Du Bois-Reymond lemma for functions of several variables, ibid.
Banach Center Publications
1996/35/1
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Pages:
221-236
Main language of publication
English
Published
1996
Exact and natural sciences