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

DOI:
https://doi.org/10.1090/S0002-9939-01-06167-6

Published electronically:
May 10, 2001

MathSciNet review:
1860504

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-01-06167-6

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