On non-negative solutions of quasilinear elliptic inequalities

A. A. Kon'kov

Izvestiya. Mathematics , Tome 63 (1999) no. 2, pp. 255-329.

Résumé

We study the solutions of the inequalities $$ Lu\geqslant F(x,u), \qquad \mathcal Lu\geqslant F(x,u), $$ where $$ L=\sum_{i,j=1}^n\frac\partial{\partial x_i}\biggl(a_{ij}(x)\frac\partial{\partial x_j}\biggr), \qquad \mathcal L=\sum_{i,j=1}^n a_{ij}(x)\frac{\partial^2}{\partial x_i\,\partial x_j}\,, $$ are differential operators of elliptic type and $F$ is some function.

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