Boundary value problems for higher order parabolic equations

Brown, Russell; Hu, Wei

doi:10.1090/S0002-9947-00-02702-1

Boundary value problems for higher order parabolic equations
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by Russell M. Brown and Wei Hu PDF

Trans. Amer. Math. Soc. 353 (2001), 809-838 Request permission

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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