Parabolic Green functions in open sets

Eklund, Neil A.

doi:10.1090/S0002-9939-1975-0509708-6

Parabolic Green functions in open sets
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by Neil A. Eklund PDF

Proc. Amer. Math. Soc. 50 (1975), 244-248 Request permission

Abstract:

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 $U$.

References

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Generalized supersolutions of parabolic equations

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Neil S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), 205–226. MR 226168, DOI 10.1002/cpa.3160210302