The existence and uniqueness for the Dirichlet problem in general domains

Ivo Babuška; Rudolf Výborný

Czechoslovak Mathematical Journal (1959)

  • Volume: 09, Issue: 1, page 130-153
  • ISSN: 0011-4642

How to cite

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Babuška, Ivo, and Výborný, Rudolf. "Die Existenz und Eindeutigkeit der Dirichletschen Aufgabe auf allgemeinen Gebieten." Czechoslovak Mathematical Journal 09.1 (1959): 130-153. <http://eudml.org/doc/11969>.

@article{Babuška1959,
author = {Babuška, Ivo, Výborný, Rudolf},
journal = {Czechoslovak Mathematical Journal},
keywords = {partial differential equations},
language = {ger},
number = {1},
pages = {130-153},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Die Existenz und Eindeutigkeit der Dirichletschen Aufgabe auf allgemeinen Gebieten},
url = {http://eudml.org/doc/11969},
volume = {09},
year = {1959},
}

TY - JOUR
AU - Babuška, Ivo
AU - Výborný, Rudolf
TI - Die Existenz und Eindeutigkeit der Dirichletschen Aufgabe auf allgemeinen Gebieten
JO - Czechoslovak Mathematical Journal
PY - 1959
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 09
IS - 1
SP - 130
EP - 153
LA - ger
KW - partial differential equations
UR - http://eudml.org/doc/11969
ER -

References

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  1. M. Brelot, La théorie moderne du potentiel, Ann. de l'Inst. Four. IV, 1952, 113- 140. (1952) Zbl0055.08903MR0059419
  2. M. Brelot, Familles de Perron et problème de Dirichlet, Acta Szeget IX, fasc. III, 1939, 133-153. (1939) Zbl0023.23302MR0000734
  3. M. Brelot, Sur le rôle du point à l'infini dans la théorie des fonctions harmoniques, Ann. Ecol Normale 61, 1944, 301 - 332. (1944) Zbl0061.22801MR0013823
  4. J. Mařík, Dirichletova úloha, Čas. pro pěst. mat. 82 (1957), 257 - 282. (1957) MR0090666
  5. И. Г. Петровский, Лекции об уравнениях с частными производными, Москва 1953. (1953) Zbl1151.94459
  6. S. Zaremba, Sur l'unicité de la solution du problème de Dirichlet, Bulletin de l'Acad. des Sc. Cracovie 1909, 561-563. (1909) 
  7. N. Wiener, 10.1002/sapm19243124, Jour. of Math. and Physics 3 (1924), 24-51. (1924) DOI10.1002/sapm19243124
  8. M. В. Келдыш, О разрешимости и устойчивости задачи Дирихле, Успехи мат. наук 8 (1941), 171-231. (1941) Zbl0179.43901MR0005249
  9. Courant R., Hilbert D., Methoden der mathematischen Physik I, II, Berlin 1931, 1937. (1931) 
  10. O. D. Kellog, Foundations of Potential Theory, Berlin 1929. (1929) 
  11. M. В. Келдыш, О задаче Дирихле, ДАН СССР 32 (1941), 308-309. (1941) Zbl0179.43901MR0011368
  12. R. Výborný, Dirichletova úloha, Čas. pro pěst. mat. 83 (1958), 99-100. (1958) 
  13. H. M. Гюнтер, Теория потенциала и ее применение к основным задачам мат. физики, Москва 1953. (1953) Zbl1151.94459
  14. L. Amerio, Teoremi di esistenza per le equazini lineari del secondo ordine di tipo ellittico nei domini illimitati, Rend. Acc. d'Italia 4 (1943), 287 - 298. (1943) MR0011876
  15. M. Krzyzański, Sur le problème de Dirichlet pour l'équation du type elliptique dans un domaine non borné, Rend. Acc. Lincei, 4 (1948), 408 - 416. (1948) MR0027118
  16. M. Krzyzański, Sur les solutions de l'équation du type elliptique discontinues sur la frontière du domaine de leur existence, Studia Mathematica 11 (1950), 95-125. (1950) MR0036420
  17. G. Tautz, 10.1007/BF01201372, Math. Zeitsch. 39 (1935), 532-559. (1935) Zbl0010.35603MR1545516DOI10.1007/BF01201372
  18. О. А. Олейнип, О задаче Дирихле для уравнений эллиптического типа, Мат. сб. 24 (1949), 3-14. (1949) Zbl1152.51302

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