Lyapunov‐type inequality to general second‐order elliptic equations

We establish Lyapunov‐type inequality for equations concerning general class of second‐order non‐symmetric elliptic operators with singular coefficients. Our approach is based on the probabilistic representation of solutions and stochastic calculus. We also discuss a Lyapunov‐type inequality for equations pertaining to second‐order symmetric operator with some regularity assumptions on the coefficients and a nonlinear Neumann boundary condition.