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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- Neil A. Eklund, Existence and representation of solutions of parabolic equations, Proc. Amer. Math. Soc. 47 (1975), 137–142. MR 361442, DOI 10.1090/S0002-9939-1975-0361442-1 —, Generalized supersolutions of parabolic equations (submitted).
- Neil A. Eklund, Convergent nets of parabolic and generalized superparabolic functions, Proc. Amer. Math. Soc. 50 (1975), 237–243. MR 509707, DOI 10.1090/S0002-9939-1975-0509707-4
- L. L. Helms, Introduction to potential theory, Pure and Applied Mathematics, Vol. XXII, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1969. MR 0261018
- Neil S. Trudinger, Pointwise estimates and quasilinear parabolic equations, Comm. Pure Appl. Math. 21 (1968), 205–226. MR 226168, DOI 10.1002/cpa.3160210302
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 50 (1975), 244-248
- MSC: Primary 35K10
- DOI: https://doi.org/10.1090/S0002-9939-1975-0509708-6
- MathSciNet review: 0509708