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

Abstract

We study the existence and nonexistence of positive singular solutions to second-order non-divergence type elliptic inequalities with measurable coefficients. We prove the existence of a critical value $p^{\ast }$ that separates the existence region from non-existence. In the critical case $p=p^{\ast }$ we show that the existence of a singular solution depends on the rate at which the coefficients stabilize at zero and we provide some optimal conditions in this setting.

24 pages