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.;
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.
Lanzani L.; Capogna L.; Brown R.M.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/873187
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