Singular Solutions for Second–order Non-divergence Type Elliptic Inequalities in Punctured Balls
نویسندگان
چکیده
We study the existence and nonexistence of positive singular solutions to second–order non-divergence type elliptic inequalities in the form N ∑ i,j=1 aij(x) ∂u ∂xi∂xj + N ∑ i=1 bi(x) ∂u ∂xi ≥ K(x)u, −∞ < p <∞, with measurable coefficients in a punctured ball BR \{0} of R , N ≥ 1. 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 (aij) and (bi) stabilize at zero and we provide some optimal conditions in this setting.
منابع مشابه
Some remarks on singular solutions of nonlinear elliptic equations. I
We study strong maximum principles for singular solutions of nonlinear elliptic and degenerate elliptic equations of second order. An application is given on symmetry of positive solutions in a punctured ball using the method of moving planes. Mathematics Subject Classification (2000). 35J69, 58J05, 53C21, 35J60.
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