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Behavior of Solutions of Quasilinear Elliptic Inequalities

Authors:

A A Kon'kov

Institution:

(1) M. V. Lomonosov State University, Russia

Abstract:

The paper considers solutions of the coercive inequalities

$Lu \geqslant F\left( {x,u} \right),\quad \mathcal{L} \geqslant F\left( {x,u} \right)$

defined on an arbitrary (possibly, unbounded) subset ℝⁿ, where n ≥ 2, L and $\mathcal{L}$ are elliptic operators of the form

$L = \sum\limits_{i,j = 1}^n {\frac{\partial }{{\partial x_i }}\left( {a_{ij} \left( x \right)\frac{\partial }{{\partial x_j }}} \right)\quad and} \quad \mathcal{L} = \sum\limits_{i,j = 1}^n {a_{ij} \left( x \right)\frac{{\partial ^2 }}{{\partial x_i \partial x_j }},}$

, and F is a certain function. __________ Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 7, Partial Differential Equations, 2004.

Keywords:

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