TY - JOUR
T1 - The mixed problem in L p for some two-dimensional Lipschitz domains
AU - Lanzani, Loredana
AU - Capogna, Luca
AU - Brown, Russell M.
N1 - Funding Information:
L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation.
PY - 2008/9
Y1 - 2008/9
N2 - 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 .
AB - 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 .
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U2 - 10.1007/s00208-008-0223-6
DO - 10.1007/s00208-008-0223-6
M3 - Article
AN - SCOPUS:46649096818
VL - 342
SP - 91
EP - 124
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 1
ER -