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 language | English |
|---|---|
| Pages (from-to) | 721-734 |
| Number of pages | 14 |
| Journal | Journal of Geometric Analysis |
| Volume | 16 |
| Issue number | 4 |
| DOIs | |
| State | Published - 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
Funding
Math SubjecCt lassifications3. 5J40. Key Wordsa ndP hrases.B iharmonic functions; Lipschitz domains; convex domains. Acknowledgemeanntsd N otes.R esearch supported by the NSE
| Funders | Funder number |
|---|---|
| NSE |
Keywords
- Biharmonic functions
- Lipschitz domains
- convex domains
ASJC Scopus subject areas
- Geometry and Topology