### Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls

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 Title: Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls Authors: Ghergu, MariusLiskevich, VitaliSobol, Zeev Permanent link: http://hdl.handle.net/10197/6149 Date: 24-Jul-2014 Abstract: We study the existence and non-existence of positive singular solutions of second-order non-divergence type elliptic inequalities of the form $\sum\limits_{i,j = 1}^N {a_{ij} (x)\frac{{\partial ^2 u}} {{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^N {b_i (x)\frac{{\partial u}} {{\partial x_i }} \geqslant K(x)u^p ,} - \infty < p - \infty ,$ with measurable coefficients in a punctured ball B R \{0} of ℝ N , N ≥ 1. We prove the existence of a critical value p* which separates the existence region from the non-existence region. We show that in the critical case p = p*, the existence of a singular solution depends on the rate at which the coefficients (a i j ) and (b i ) stabilize at zero, and we provide some optimal conditions in this setting. Type of material: Journal Article Publisher: Springer Keywords: Non-divergence semi-linear equation;Singular solutions;Punctured ball;Critical exponent DOI: 10.1007/s11854-014-0020-y Language: en Status of Item: Peer reviewed Appears in Collections: Mathematics and Statistics Research Collection

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