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

Dariusz Idczak

Banach Center Publications (1996)

  • Volume: 35, Issue: 1, page 221-236
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Idczak, Dariusz. "The generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order." Banach Center Publications 35.1 (1996): 221-236. <http://eudml.org/doc/251316>.

@article{Idczak1996,
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.},
author = {Idczak, Dariusz},
journal = {Banach Center Publications},
keywords = {Du Bois-Reymond lemma; functions of two variables; higher-order partial derivatives},
language = {eng},
number = {1},
pages = {221-236},
title = {The generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order},
url = {http://eudml.org/doc/251316},
volume = {35},
year = {1996},
}

TY - JOUR
AU - Idczak, Dariusz
TI - The generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order
JO - Banach Center Publications
PY - 1996
VL - 35
IS - 1
SP - 221
EP - 236
AB - 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.
LA - eng
KW - Du Bois-Reymond lemma; functions of two variables; higher-order partial derivatives
UR - http://eudml.org/doc/251316
ER -

References

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  1. [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. Zbl0959.49004
  2. [2] L. A. Lusternik and W. I. Sobolew, Elements of Functional Analysis, Warsaw 1959, (Polish). 
  3. [3] J. Mawhin, Problèmes de Dirichlet Variationnels Non-Linéaires, L'Université de Montréal, 1987. 
  4. [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). Zbl0802.34007
  5. [5] S. Walczak, On the Du Bois-Reymond lemma for functions of several variables, ibid. Zbl0809.49004

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