Geodesic
On the solution of some non-local problems
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 487-498 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution of these problems is proved. The solutions are constructed in an explicit form.
This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution of these problems is proved. The solutions are constructed in an explicit form.
Classification : 35J05, 35J25
Keywords: non-local problem; Poisson equation; discrete Fourier transform 
@article{CMJ_2004_54_2_a19,
     author = {Criado, F. and Criado, F., Jr. and Odishelidze, N.},
     title = {On the solution of some non-local problems},
     journal = {Czechoslovak Mathematical Journal},
     pages = {487--498},
     year = {2004},
     volume = {54},
     number = {2},
     mrnumber = {2059268},
     zbl = {1080.35015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a19/}
}
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Criado, F.; Criado, F., Jr.; Odishelidze, N. On the solution of some non-local problems. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 487-498. http://geodesic.mathdoc.fr/item/CMJ_2004_54_2_a19/