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

 

Boundary value problems for higher order parabolic equations


Authors: Russell M. Brown and Wei Hu
Journal: Trans. Amer. Math. Soc. 353 (2001), 809-838
MSC (2000): Primary 35K35
Published electronically: October 19, 2000
MathSciNet review: 1804519
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Abstract:

We consider a constant coefficient parabolic equation of order $2m$ and establish the existence of solutions to the initial-Dirichlet problem in cylindrical domains. The lateral data is taken from spaces of Whitney arrays which essentially require that the normal derivatives up to order $m-1$ lie in $L^2$ with respect to surface measure. In addition, a regularity result for the solution is obtained if the data has one more derivative. The boundary of the space domain is given by the graph of a Lipschitz function. This provides an extension of the methods of Pipher and Verchota on elliptic equations to parabolic equations.


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Additional Information

Russell M. Brown
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
Email: rbrown@pop.uky.edu

Wei Hu
Affiliation: Department of Mathematics and Computer Science, Houghton College, Houghton, New York 14744
Email: weih@houghton.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02702-1
PII: S 0002-9947(00)02702-1
Received by editor(s): June 2, 1998
Published electronically: October 19, 2000
Dedicated: This paper is dedicated to Gene Fabes
Article copyright: © Copyright 2000 American Mathematical Society