Reflection principles for the iterated Helmholtz equation.
J. B. Díaz (1975)
Collectanea Mathematica
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J. B. Díaz (1975)
Collectanea Mathematica
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M. Greguš (1974)
Annales Polonici Mathematici
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Tutschke, Wolfgang (2002)
Boletín de la Asociación Matemática Venezolana
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K. S. Padmanabhan, R. Parvatham (1976)
Annales Polonici Mathematici
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B. Przeradzki (1989)
Annales Polonici Mathematici
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Michał Kisielewicz (1997)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Some sufficient conditions for the existence of solutions to boundary value problem for differential inclusions are given.
Andrzej Czarnecki, Marcin Kulczycki, Wojciech Lubawski (2011)
Annales Polonici Mathematici
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This article gives a short and elementary proof of the fact that the connectedness of the boundary of an open domain in ℝⁿ is equivalent to the connectedness of its complement.
Józef Wenety Myjak (1973)
Annales Polonici Mathematici
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L. Aizenberg (1995)
Banach Center Publications
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Jenkinson, Oliver (2000)
Experimental Mathematics
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M. Benchora, S. K. Ntouyas (2001)
Matematički Vesnik
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Przemysław Górka (2007)
Colloquium Mathematicae
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We examine an elliptic equation in a domain Ω whose boundary ∂Ω is countably (m-1)-rectifiable. We also assume that ∂Ω satisfies a geometrical condition. We are interested in an overdetermined boundary value problem (examined by Serrin [Arch. Ration. Mech. Anal. 43 (1971)] for classical solutions on domains with smooth boundary). We show that existence of a solution of this problem implies that Ω is an m-dimensional Euclidean ball.
Evgeny B. Dynkin (1965)
Annales de l'institut Fourier
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Nous étudions le problème de Neumann avec dérivée oblique dans un domaine 2-dimensionnel borné par un contour régulier . Le champ vectoriel donné sur peut être tangent à en un nombre fini de points. En utilisant une extension de la méthode de Martin nous trouvons toutes les solutions positives de ce problème aux valeurs limites.