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A Hardy inequality in a twisted Dirichlet-Neumann waveguide

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    0311859 - ÚJF 2009 RIV DE eng J - Journal Article
    Kovařík, Hynek - Krejčiřík, David
    A Hardy inequality in a twisted Dirichlet-Neumann waveguide.
    [Hardyho nerovnost ve zkroucenem direchletovsko-neumannovskem vlnovodu.]
    Mathematische Nachrichten. Roč. 281, č. 8 (2008), s. 1159-1168. ISSN 0025-584X. E-ISSN 1522-2616
    R&D Projects: GA MŠMT LC06002
    Institutional research plan: CEZ:AV0Z10480505
    Keywords : Laplacian * Dirichlet and Neumann boundary conditions * twist
    Subject RIV: BE - Theoretical Physics
    Impact factor: 0.537, year: 2008

    We consider the Laplacian in a straight strip, subject to a combination of Dirichlet and Neumann boundary conditions. We show that a switch of the respective boundary conditions leads to a Hardy inequality for the Laplacian. As a byproduct of our method, we obtain a simple proof of a theorem of Dittrich and Kriz [5].

    Ukazujeme, ze nahle prepnuti dirichletovskych a neumannovskych hranicnich podminek na rovnem nekonecnem pasku vede k Hardyho nerovnosti pro odpovidajici laplacian. Jako vedlejsi vysledek nasi metody dostaneme jednoduchy dukaz teoremu Dittricha a Krize o neexistenci vazanych stavu.
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