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Behavior of Solutions of Quasilinear Elliptic Inequalities

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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.

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  1. M. V. Lomonosov State University, Russia

    A. A. Kon'kov

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Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 7, Partial Differential Equations, 2004.

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Kon'kov, A.A. Behavior of Solutions of Quasilinear Elliptic Inequalities. J Math Sci 134, 2073–2237 (2006). https://doi.org/10.1007/s10958-006-0096-8

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