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Hardy Potentials and Quasi-linear Elliptic Problems Having Natural Growth Terms

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Elliptic and Parabolic Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 63))

Abstract

In this paper we consider nonlinear boundary value problems whose simplest model is the following:

$${\left\{ {\begin{array}{*{20}c} {\Delta u + = \gamma |\nabla u|^2 + \frac{A} {{|x|^2 }}} & {in\;\Omega } & {\left( {\gamma ,\;A\; \in \;\mathbb{R}} \right)} \\ {\;\quad \quad \quad \quad \quad u = 0} & {\quad on\;\partial \Omega .} & {} \\ \end{array} } \right.}$$

where Ω is a bounded open set in \(\mathbb{R}^N \), N > 2.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma 1, Piazza A. Moro 2, I-00185, Roma, Italia

    Lucio Boccardo

Authors
  1. Lucio Boccardo
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051, Basel, Switzerland

    Catherine Bandle

  2. Ecole des hautes études en sciences sociales (EHESS), CAMS, 54, Boulevard Raspail, 75006, Paris, France

    Henri Berestycki

  3. Faculté des Sciences et Techniques, Université de Haute-Alsace, 4 rue des frères Lumières, 68093, Mulhouse Cedex, France

    Bernard Brighi

  4. Laboratoire de Gestion des Risques et Environnement, Université de Haute-Alsace, 25, rue de Chemnitz, 68200, Mulhouse, France

    Alain Brillard

  5. Angewandte Mathematik, Universität Zürich, Winterthurerstr. 190, 8057, Zürich, Switzerland

    Michel Chipot

  6. Département de mathématiques, Université de Paris-Sud, Bâtiment 425, 91405, Orsay, France

    Jean-Michel Coron

  7. Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II”, Via Cintia, 80126, Napoli, Italy

    Carlo Sbordone

  8. Department of Mathematics, Technion — Israel Institute of Technology, 32000, Haifa, Israel

    Itai Shafrir

  9. CNR-IAC, Viale del Policlinico, 137, 00161, Roma, Italy

    Vanda Valente

  10. Dipartimento di metodi e modelli matematici per le Scienze Aplicate, Università di Roma “La Sapienza”, Via A. Scarpa 16, 00161, Roma, Italy

    Giorgio Vergara Caffarelli

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Boccardo, L. (2005). Hardy Potentials and Quasi-linear Elliptic Problems Having Natural Growth Terms. In: Bandle, C., et al. Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 63. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7384-9_8

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