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Overdetermined anisotropic elliptic problems

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Abstract

A symmetry result is established for solutions to overdetermined anisotropic elliptic problems in variational form, which extends Serrin’s theorem dealing with the isotropic radial case. The involved anisotropy arises from replacing the Euclidean norm of the gradient with an arbitrary norm in the associated variational integrals. The resulting symmetry of the solutions is that of the so-called Wulff shape.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni per l’Architettura, Università di Firenze, Piazza Ghiberti 27, 50122, Florence, Italy

    Andrea Cianchi

  2. Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, 50134, Florence, Italy

    Paolo Salani

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  1. Andrea Cianchi
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  2. Paolo Salani
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Correspondence to Andrea Cianchi.

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Cianchi, A., Salani, P. Overdetermined anisotropic elliptic problems. Math. Ann. 345, 859–881 (2009). https://doi.org/10.1007/s00208-009-0386-9

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  • DOI: https://doi.org/10.1007/s00208-009-0386-9

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