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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The behavior of the heat operator
on weighted Sobolev spaces


Authors: G. N. Hile and C. P. Mawata
Journal: Trans. Amer. Math. Soc. 350 (1998), 1407-1428
MSC (1991): Primary 35B45; Secondary 35A05, 35J60
MathSciNet review: 1467466
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Abstract: Denoting by ${\mathcal{H}}$ the heat operator in $R^{n+1}$, we investigate its properties as a bounded operator from one weighted Sobolev space to another. Our main result gives conditions on the weights under which ${\mathcal{H}}$ is an injection, a surjection, or an isomorphism. We also describe the range and kernel of ${\mathcal{H}}$ in all the cases. Our results are analogous to those obtained by R. C. McOwen for the Laplace operator in $R^{n}$.


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Additional Information

G. N. Hile
Affiliation: University of Hawaii, Manoa, 2565 The Mall, Honolulu, Hawaii 96822
Email: hile@math.hawaii.edu

C. P. Mawata
Affiliation: University of Tennessee, Chattanooga, 615 McCallie Avenue, Chattanooga, Tennessee 37403
Email: cmawata@cecasun.utc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02140-0
PII: S 0002-9947(98)02140-0
Received by editor(s): April 12, 1996
Article copyright: © Copyright 1998 American Mathematical Society