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

 

Polynomial growth solutions of uniformly elliptic operators of non-divergence form


Authors: Peter Li and Jiaping Wang
Journal: Proc. Amer. Math. Soc. 129 (2001), 3691-3699
MSC (2000): Primary 35J15
Published electronically: May 10, 2001
MathSciNet review: 1860504
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Abstract:

We give an explicit description of polynomial growth solutions to a uniformly elliptic operator of non-divergence form with periodic coefficients on the Euclidean spaces. We also show that the solutions are of one-to-one correspondence to harmonic polynomials if the coefficients of the operator are continuous.


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Additional Information

Peter Li
Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875
Email: pli@math.uci.edu

Jiaping Wang
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: jiaping@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06167-6
PII: S 0002-9939(01)06167-6
Received by editor(s): May 2, 2000
Published electronically: May 10, 2001
Additional Notes: The first author’s research was partially supported by NSF grant #DMS-9971418
The second author’s research was partially supported by NSF grant #DMS-9704482
Communicated by: Bennett Chow
Article copyright: © Copyright 2001 American Mathematical Society