Nonnegative solutions of some quasilinear elliptic inequalities and applications

L. D'Ambrosio   ; E. Mitidieri

Sbornik. Mathematics, Tome 201 (2010) no. 6, pp. 855-871

Résumé

Let $f\colon \mathbb R\to\mathbb R$ be a continuous function. It is shown that under certain assumptions on $f$ and $A\colon \mathbb R\to\mathbb R_+$ weak $\mathscr C^1$ solutions of the differential inequality $-\operatorname{div}(A(|\nabla u|)\nabla u)\geqslant f(u)$ on $\mathbb R^N$ are nonnegative. Some extensions of the result in the framework of subelliptic operators on Carnot groups are considered. Bibliography: 19 titles.

Détail

Keywords: differential inequalities, $p$-Laplacian, subelliptic operators, Carnot groups.
Mots-clés : nonnegative solutions

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