Abstract
Using Maz ’ya type integral identities with power weights, we obtain new boundary estimates for biharmonic functions on Lipschitz and convex domains in ℝn. Forn ≥ 8, combinedwitharesultin[18], these estimates lead to the solvability of the Lp 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 Lp Dirichlet problem is uniquely solvable for any 2 − ε < p < ∞ and n ≥ 4.
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Communicated by David Jerison
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Shen, Z. On estimates of biharmonic functions on Lipschitz and convex domains. J Geom Anal 16, 721–734 (2006). https://doi.org/10.1007/BF02922138
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DOI: https://doi.org/10.1007/BF02922138