New Poincaré inequalities from old.
Buckley, Stephen M., Koskela, Pekka (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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Buckley, Stephen M., Koskela, Pekka (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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Mokeeva, N.V. (2005)
Zapiski Nauchnykh Seminarov POMI
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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.
Endre Makai (1959)
Czechoslovak Mathematical Journal
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Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
Roberto Peirone (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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We state that in opportune tubular domains any two points are connected by a bounce trajectory and that there exist non-trivial periodic bounce trajectories.
Duduchava, R., Silbermann, B. (2000)
Memoirs on Differential Equations and Mathematical Physics
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Brian D. Sleeman, Chen Hua (2000)
Revista Matemática Iberoamericana
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A fundamental question raised by M. Kac in 1966 is: Must two isospectral planar domains necessarily be isometric? Following a long history of investigation C. Gordon, D. L. Webb and S. Wolpert in 1992 finally proved that the answer is no. By using the idea of transposition maps one can construct a wide class of planar domains with piecewise continuous boundaries which are isospectral but non-isometric. In this note we study the Kac question in relation to domains with fractal boundaries...
Väisälä, Jussi (1994)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Tomasz Dłotko (1980)
Annales Polonici Mathematici
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Maciej Skwarczyński
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CONTENTSPRELIMINARY REMARKS........................................................................................ 5 Introduction..................................................................................................... 5 Basic definitions, examples and facts............................................................... 8I. LU QI-KENQ DOMAINS........................................................................................... 13 Some properties of Lu Qi-keng domains.....................................................
Stefan Bergman (1977)
Annales Polonici Mathematici
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Neil M. Wigley (1970)
Mathematische Zeitschrift
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