On the solution of some non-local problems

F. Criado; Jr. Criado, F.; N. Odishelidze

Czechoslovak Mathematical Journal (2004)

  • Volume: 54, Issue: 2, page 487-498
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Criado, F., Criado, F., Jr., and Odishelidze, N.. "On the solution of some non-local problems." Czechoslovak Mathematical Journal 54.2 (2004): 487-498. <http://eudml.org/doc/30877>.

@article{Criado2004,
abstract = {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.},
author = {Criado, F., Criado, F., Jr., Odishelidze, N.},
journal = {Czechoslovak Mathematical Journal},
keywords = {non-local problem; Poisson equation; discrete Fourier transform; nonlocal problem; Poisson equation; discrete Fourier transform},
language = {eng},
number = {2},
pages = {487-498},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the solution of some non-local problems},
url = {http://eudml.org/doc/30877},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Criado, F.
AU - Criado, F., Jr.
AU - Odishelidze, N.
TI - On the solution of some non-local problems
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 487
EP - 498
AB - 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.
LA - eng
KW - non-local problem; Poisson equation; discrete Fourier transform; nonlocal problem; Poisson equation; discrete Fourier transform
UR - http://eudml.org/doc/30877
ER -

References

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  5. Sulla integrazione della equazione Δ 2 u = 0 , Brioschi Ann. VI (1873), 305–345. (Italian) (1873) 
  6. Solution of nonlocal problems in plane elasticity theory, Current Problems of Mathematical Physics, Vol. 2. Transactions of All-Union Symposium, Gos. Univ., Tbilisi, 1987, pp. 295–302, 394. (Russian) (1987) MR0991842
  7. 10.1080/17476939208814560, Complex Variables Theory Appl. 19 (1992), 71–79. (1992) Zbl0779.35019MR1228330DOI10.1080/17476939208814560
  8. P.D.E. in Clifford Analysis, Longman, Addison Wesley, 1998. (1998) MR1697655
  9. Sur une equation aux derivées partielles due type composite, Ark. Mat. Astron. Fys. 25A (1937), no. 21, 1–11. (1937) 

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