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

• Autorzy: Dariusz Idczak
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 35
• Numer: 1
• Strony: 221-236

Daty

wydano

1996

Twórcy

autor

Dariusz Idczak

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

Bibliografia

• [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.