Geodesic
On the solution of some non-local problems
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 2, pp. 487-498.

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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.
Classification : 35J05, 35J25
Keywords: non-local problem; Poisson equation; discrete Fourier transform 
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     title = {On the solution of some non-local problems},
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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/