Affiliation:
1. Department of Mathematics Indian Institute of Technology Gandhinagar Gandhinagar, Gujarat India
Abstract
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.
Reference42 articles.
1. Two‐dimensional Brownian motion and harmonic functions;Kakutani S.;Proc. Imp. Acad. Tokyo,1994
2. Time‐reversal and elliptic boundary value problems;Chen Z. Q.;Ann. Probab.,2009
3. Positive Harmonic Functions and Diffusion
4. Diffusion processes second order elliptic operators with singular coefficients for lower order terms;Chen Z. Q.;Math. Ann.,1995