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Isoperimetric inequalities for a class of nonlinear parabolic equations

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Abstrac

Existence theorems and a priori bounds for a class of nonlinear parabolic equations are established. By means of an iteration process and symmetrization methods the solution in an arbitrary domain is compared with the one for the sphere of the same volume. It is shown that among all domains of given volume the sphere is the least stable.

Zusammenfassung

Mit Hilfe von Symmetrisierungen und Iterationsmethoden werden Existenzsätze und a priori Schranken für eine Klasse von nichtlinearen parabolischen Differentiagleichungen hergeleitet. Die Lösung für ein allgemeines Gebiet wird mit derjenigen für die Kugel vom gleichen Volumen verglichen. Es zeigt sich insbesondere, dass unter allen Gebieten mit demselben Volumen die Kugel am wenigsten stabil ist.

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Authors and Affiliations

  1. Dept. of Mathematics, The University, Basel, Switzerland

    Catherine Bandle

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  1. Catherine Bandle
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Bandle, C. Isoperimetric inequalities for a class of nonlinear parabolic equations. Journal of Applied Mathematics and Physics (ZAMP) 27, 377–384 (1976). https://doi.org/10.1007/BF01590510

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  • DOI: https://doi.org/10.1007/BF01590510

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