Transactions of the American Mathematical Society

Author(s): Russell M. Brown; Wei Hu
Journal: Trans. Amer. Math. Soc. 353 (2001), 809-838.
MSC (2000): Primary 35K35
Posted: October 19, 2000
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We consider a constant coefficient parabolic equation of order

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

lie in

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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35K35

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: 10.1090/S0002-9947-00-02702-1
PII: S 0002-9947(00)02702-1
Received by editor(s): June 2, 1998
Posted: October 19, 2000
Dedicated: This paper is dedicated to Gene Fabes
Copyright of article: Copyright 2000, American Mathematical Society

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