ESTIMATES OF HEAT KERNELS FOR A CLASS OF SECOND-ORDER ELLIPTIC OPERATORS WITH APPLICATIONS TO SEMI-LINEAR INEQUALITIES IN EXTERIOR DOMAINS
Vladimir Kondratiev, Vitali Liskevich, Zeev Sobol, Oleksiy Us · Journal of the London Mathematical Society · 2004
Fundamental solutions to second-order parabolic and elliptic equations with lower-order terms are studied. New sufficient conditions on the coefficients of the lower-order terms are given that guarantee the validity of two-sided Gaussian bounds on the fundamental solution to the parabolic equation, locally and globally in time. As an application, the problem of existence and non-existence of positive solutions to a class of semi-linear equations is studied.