Abstract
We consider the mixed problem, {Δ u = 0 in Ω ∂u = f N on N u = fD on D in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data, f D , has one derivative in L p (D) of the boundary and the Neumann data, f N , is in L p (N). We find a p 0 > 1 so that for p in an interval (1, p 0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L p .
| Original language | English (US) |
|---|---|
| Pages (from-to) | 91-124 |
| Number of pages | 34 |
| Journal | Mathematische Annalen |
| Volume | 342 |
| Issue number | 1 |
| DOIs | |
| State | Published - Sep 1 2008 |
| Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)
Fingerprint Dive into the research topics of 'The mixed problem in L <sup>p</sup> for some two-dimensional Lipschitz domains'. Together they form a unique fingerprint.
Cite this
Lanzani, L., Capogna, L., & Brown, R. M. (2008). The mixed problem in L p for some two-dimensional Lipschitz domains. Mathematische Annalen, 342(1), 91-124. https://doi.org/10.1007/s00208-008-0223-6