Asymptotics of solutions of second order parabolic equations near conical points and edges

The authors consider the first boundary value problem for a second order parabolic equation with variable coefficients in a domain with conical points or edges. In the first part of the paper, they study the Green function for this problem in the domain K x Rn-m, where K is an infinite cone in R-m, 2 less than= m less than= n. They obtain the asymptotics of the Green function near the vertex ( n = m) and edge ( n greater than m), respectively. This result is applied in the second part of the paper, which deals with the initial-boundary value problem in this domain. Here, the right-hand side f of the differential equation belongs to a weighted L-p space. At the end of the paper, the initial-boundary value problem in a bounded domain with conical points or edges is studied