The Mixed Boundary Problem in L and Hardy spaces for Laplace’s Equation on a Lipschitz Domain
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چکیده
We study the boundary regularity of solutions of the mixed problem for Laplace’s equation in a Lipschitz graph domain Ω whose boundary is decomposed as ∂Ω = N ∪ D, where N ∩ D = ∅. For a subclass of these domains, we show that if the Neumann data g is in Lp(N) and if the Dirichlet data f is in the Sobolev space L(D), for 1 < p < 2, then the mixed boundary problem has a unique solution u for which N(∇u) ∈ Lp(∂Ω), where N(∇u) is the non-tangential maximal function of the gradient of u.
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تاریخ انتشار 2001