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Keywords:
uniformly elliptic; linear boundary value problems
uniformly elliptic; linear boundary value problems
Summary:
The author solves a mixed boundary value problem for linear partial differential equations of the elliptic type in a multiply connected domain. Dirichlet conditions are given on the components of the boundary of the domain up to some additive constants which are not known a priori. These constants are to be determined, together with the solution of the boundary value problem, to fulfil some additional conditions. The results are immediately applicable in hydrodynamics to the solution of problems of stream fields round groups of profiles.
References:
[1] L. Bers F. John M. Schechter: Partial differential equations. Interscience publishers, New York - London- Sydney, 1964. MR 0163043
[2] M. Feistauer: On two-dimensional and three-dimensional axially-symmetric rotational flows of an ideal incompressible fluid. Apl. mat. 22 (1977) No 3, 199-214. MR 0436748 | Zbl 0373.76022
[3] M. Feistauer: Solution of axially-symmetric stream fields in multiply connected domains. Technical research report, ŠKODA Plzeň, 1977 (in Czech).
[4] K. Jacob: Berechnung der inkompressiblen Potentialströmung für Einzel- und Gitterprofile nach einer Variante des Martensens-Verfahrens. Bericht 63 RO2 der Aerodynamischen Versuchsanstalt Göttingen, 1963.
[5] О. А. Ладыженская H. H. Уральцева: Линейные и квазилинейные уравнения эллиптического типа. Наука, Москва, 1973. Zbl 1221.53041
[6] Л. Г. Лойцянский: Механика жидкости и газа. Физматриз, Москва, 1973. Zbl 1170.01397
[7] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague, 1967. MR 0227584
[8] Z. Vlášek: Plane potential flow of an ideal incompressible fluid round groups of profiles and cascades of profiles. PhD thesis, Faculty of Mathematics and Physics, Prague, 1973 (in Czech).
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