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Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights

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An Erratum to this article was published on 08 February 2008

Non-existence results for non-negative distribution entire solutions of singular quasilinear elliptic differential inequalities with weights are established. Such inequalities include the capillarity equation with varying gravitational field h, as well as the general p-Poisson equation of radiative cooling with varying heat conduction coefficient g and varying radiation coefficient h. Since we deal with inequalities and positive weights, it is not restrictive to assume h radially symmetric. Theorem 1 extends in several directions previous results and says that solely entire large solutions can exist, while Theorem 2 shows that in the p-Laplacian case positive entire solutions cannot exist. The results are based on some qualitative properties of independent interest.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy

    Roberta Filippucci & Patrizia Pucci

  2. Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 29100, Milano, Italy

    Marco Rigoli

Authors
  1. Roberta Filippucci
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  2. Patrizia Pucci
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  3. Marco Rigoli
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Correspondence to Roberta Filippucci.

Additional information

Communicated by C. A. Stuart

An erratum to this article can be found at http://dx.doi.org/10.1007/s00205-007-0105-1

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Filippucci, R., Pucci, P. & Rigoli, M. Non-existence of Entire Solutions of Degenerate Elliptic Inequalities with Weights. Arch Rational Mech Anal 188, 155–179 (2008). https://doi.org/10.1007/s00205-007-0081-5

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  • DOI: https://doi.org/10.1007/s00205-007-0081-5

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