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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Parabolic Green functions in open sets


Author: Neil A. Eklund
Journal: Proc. Amer. Math. Soc. 50 (1975), 244-248
MSC: Primary 35K10
MathSciNet review: 0509708
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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$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0509708-6
PII: S 0002-9939(1975)0509708-6
Keywords: Second order parabolic operator, Green functions, bounded domains
Article copyright: © Copyright 1975 American Mathematical Society