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Faber-Krahn Inequality for Anisotropic Eigenvalue Problems with Robin Boundary Conditions

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Abstract

In this paper we study the main properties of the first eigenvalue λ 1(Ω) and its eigenfunctions of a class of highly nonlinear elliptic operators in a bounded Lipschitz domain Ω ⊂ ℝ n , assuming a Robin boundary condition. Moreover, we prove a Faber-Krahn inequality for λ 1(Ω).

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni R. Caccioppoli, Complesso di Monte Sant’Angelo, Università degli studi di Napoli Federico II, 80126, Via Cintia, Napoli, Italia

    Francesco Della Pietra & Nunzia Gavitone

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  1. Francesco Della Pietra
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  2. Nunzia Gavitone
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Correspondence to Francesco Della Pietra.

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Della Pietra, F., Gavitone, N. Faber-Krahn Inequality for Anisotropic Eigenvalue Problems with Robin Boundary Conditions. Potential Anal 41, 1147–1166 (2014). https://doi.org/10.1007/s11118-014-9412-y

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