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

100%
Idczak D.
Banach Center Publications
|
1996
|
tom 35
|
nr 1
221-236
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.
2
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Functions of several variables of finite variation and their differentiability

100%
Idczak D.
Annales Polonici Mathematici
|
1994-1995
|
tom 60
|
nr 1
47-56
EN
Some differentiability properties of functions of several variables of finite variation are investigated.
3
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On a class of diffeomorphisms defined by integro-differential operators

51%
Idczak D., Skowron A., Walczak S.
Banach Center Publications
|
2014
|
tom 101
|
nr 1
77-86
EN
We study an integro-differential operator Φ: H̅¹ → L² of Fredholm type and give sufficient conditions for Φ to be a diffeomorphism. An application to functional equations is presented.
4
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Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem

51%
Idczak D., Majewski M., Walczak S.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 1
29-44
EN
In the present paper, some results concerning the continuous dependence of optimal solutions and optimal values on data for an optimal control problem associated with a Goursat-Darboux problem and an integral cost functional are derived.
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