Parabolic Green Functions in Open Sets
Neil A. Eklund · Proceedings of the American Mathematical Society · 1975
Consider the parabolic operator $L$ defined by $Lu = {u_t} - \{ {a_{ij}}u{,_i} + {d_j}u\} {,_j} - {b_j}u{,_j} - cu$ in an open set $U$ in ${E^n} \times (0,T)$. By using the natural abstraction of the notion of a Green function, the author obtains the existence of a unique Green function for $Lu = 0$ on $U$.