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The Journal of Geometric Analysis

, Volume 16, Issue 4, pp 721–734 | Cite as

On estimates of biharmonic functions on Lipschitz and convex domains

  • Zhongwei Shen
Article

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.

Math Subject Classifications

35J40 

Key Words and Phrases

Biharmonic functions Lipschitz domains convex domains 

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Copyright information

© Mathematica Josephina, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KentuckyLexington

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