A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities |
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Authors: | Lorenzo D'Ambrosio Enzo Mitidieri |
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Institution: | a Dipartimento di Matematica, Università degli Studi di Bari, via E. Orabona, 4, I-70125 Bari, Italy b Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, via A. Valerio, 12/1, I-34127 Trieste, Italy |
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Abstract: | A priori bounds for solutions of a wide class of quasilinear degenerate elliptic inequalities are proved. As an outcome we deduce sharp Liouville theorems. Our investigation includes inequalities associated to p-Laplacian and the mean curvature operators in Carnot groups setting. No hypotheses on the solutions at infinity are assumed. General results on the sign of solutions for quasilinear coercive/noncoercive inequalities are considered. Related applications to population biology and chemical reaction theory are also studied. |
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Keywords: | Quasilinear operators A priori estimate Liouville theorem Positivity Elliptic inequality Carnot group |
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