Singular solutions for second-order non-divergence type elliptic   inequalities in punctured balls
  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 $p^*$ that separates the existence region from non-existence. In the critical case $p=p^*$ 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. 
Marius Ghergu, Vitali Liskevich, Zeev Sobol
math.AP