On Estimates of Biharmonic Functions on Lipschitz and Convex Domains

Details On Estimates of Biharmonic Functions on Lipschitz and Convex Domains On Estimates of Biharmonic Functions on Lipschitz and Convex Domains

2005-10-03

arxiv.org/abs/math/0510053v1

Mathematics

Analysis of PDEs

Scientific paper

Using Maz'ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in $R^n$. For $n\ge 8$, combined with a result in \cite{S2}, these estimates lead to the solvability of the $L^p$ Dirichlet problem for the biharmonic equation on Lipschitz domains for a new range of $p$. In the case of convex domains, the estimates allow us to show that the $L^p$ Dirichlet problem is uniquely solvable for any $2-\e

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