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An approach via symmetrization methods to nonlinear elliptic problems with a lower order term

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Abstract

In this paper we consider a class of nonlinear elliptic problems of the type

$$ \left\{ \begin{gathered} - div(a(x,\nabla u)) - div(\Phi (x,u)) = fin\Omega \hfill \\ u = 0on\partial \Omega , \hfill \\ \end{gathered} \right. $$

where Ω is a bounded open subset of R N, N ≥ 2, f is a L 1 (Ω) function or a Radon measure with bounded total variation. We fix some structural conditions on a and Φ to prove uniqueness results when f ∈ L 1 (Ω).

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S.Angelo, via Cintia, 80126, Napoli, Italy

    Rosaria Di Nardo

  2. Dipartimento di Matematica, Seconda Università di Napoli, Via Vivaldi, 81100, Caserta, Italy

    Adamaria Perrotta

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  1. Rosaria Di Nardo
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  2. Adamaria Perrotta
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Correspondence to Rosaria Di Nardo.

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Di Nardo, R., Perrotta, A. An approach via symmetrization methods to nonlinear elliptic problems with a lower order term. Rend. Circ. Mat. Palermo 59, 303–317 (2010). https://doi.org/10.1007/s12215-010-0024-0

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