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 . © 2008 Springer-Verlag.
The mixed problem in L p for some two-dimensional Lipschitz domains / Lanzani L.; Capogna L.; Brown R.M.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - ELETTRONICO. - 342:1(2008), pp. 91-124. [10.1007/s00208-008-0223-6]
The mixed problem in L p for some two-dimensional Lipschitz domains
Lanzani L.;
2008
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 . © 2008 Springer-Verlag.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
