Nonexistence of Entire Solutions of Degenerate Elliptic Inequalities with Weights
 Roberta Filippucci,
 Patrizia Pucci,
 Marco Rigoli
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Get AccessNonexistence results for nonnegative 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 pPoisson 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 pLaplacian case positive entire solutions cannot exist. The results are based on some qualitative properties of independent interest.
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 Title
 Nonexistence of Entire Solutions of Degenerate Elliptic Inequalities with Weights
 Journal

Archive for Rational Mechanics and Analysis
Volume 188, Issue 1 , pp 155179
 Cover Date
 20080401
 DOI
 10.1007/s0020500700815
 Print ISSN
 00039527
 Online ISSN
 14320673
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Roberta Filippucci ^{(1)}
 Patrizia Pucci ^{(1)}
 Marco Rigoli ^{(2)}
 Author Affiliations

 1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123, Perugia, Italy
 2. Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 29100, Milano, Italy