# 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 (1996)

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

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topIdczak, 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

top- [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] 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). Zbl0802.34007
- [5] S. Walczak, On the Du Bois-Reymond lemma for functions of several variables, ibid. Zbl0809.49004

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