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A Priori Estimates and Comparison Principle for Some Nonlinear Elliptic Equations

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Geometric Properties for Parabolic and Elliptic PDE's

Part of the book series: Springer INdAM Series ((SINDAMS,volume 2))

Abstract

We present a priori estimates and comparison principle for second order quasilinear elliptic operators in divergence form with a first order term. We deduce existence and uniqueness results for weak solutions or “solution obtained as limit of approximations” to Dirichlet problems related to these types of operators when data belong to suitable Lorentz spaces. Moreover it is also shown how the summability of these solutions increases when the summability of the datum increases.

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Authors and Affiliations

  1. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Complesso di Monte S. Angelo, 80126, Napoli, Italy

    Anna Mercaldo

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  1. Anna Mercaldo
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Correspondence to Anna Mercaldo .

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Editors and Affiliations

  1. Dipartimento di Matematica "U. Dini", Università di Firenze, Viale Morgagni 67/A, Firenze, 50124, Italy

    Rolando Magnanini

  2. Graduate School of Information Sciences, Division of Mathematics, Tohoku University, Sendai, 980-8579, Japan

    Shigeru Sakaguchi

  3. , Dipartimento di Matematica ed Applicazio, Università di Napoli Federico II, Via Cintia, Monte S. Angelo, Napoli, 80126, Italy

    Angelo Alvino

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Mercaldo, A. (2013). A Priori Estimates and Comparison Principle for Some Nonlinear Elliptic Equations. In: Magnanini, R., Sakaguchi, S., Alvino, A. (eds) Geometric Properties for Parabolic and Elliptic PDE's. Springer INdAM Series, vol 2. Springer, Milano. https://doi.org/10.1007/978-88-470-2841-8_14

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