On estimates of biharmonic functions on Lipschitz and convex domains

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16 Scopus citations

Abstract

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. Forn ≥ 8, combinedwitharesultin[18], 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 - ε < p < ∞ and n ≥ 4.

Original languageEnglish
Pages (from-to)721-734
Number of pages14
JournalJournal of Geometric Analysis
Volume16
Issue number4
DOIs
StatePublished - 2006

Bibliographical note

Funding Information:
Math SubjecCt lassifications3. 5J40. Key Wordsa ndP hrases.B iharmonic functions; Lipschitz domains; convex domains. Acknowledgemeanntsd N otes.R esearch supported by the NSE

Keywords

  • Biharmonic functions
  • Lipschitz domains
  • convex domains

ASJC Scopus subject areas

  • Geometry and Topology

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