Regularity of weak solutions of elliptic and parabolic equations with some critical or supercritical potentials

Previously P. Baras and J. A. Goldstein [3] treated the case when A<0, (aij)=I and β=0 for which they show that there does not exist any regular positive solution or singular positive solutions, depending on the size of |A|. When A>0, β=0 and (aij)=I, P. D. Milman and Y. A. Semenov [7,8] obtain bounds for the heat kernel.