On estimates of biharmonic functions on Lipschitz and convex domains
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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, 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.
Math Subject Classifications35J40
Key Words and PhrasesBiharmonic functions Lipschitz domains convex domains
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