Abstract
We consider the mixed problem,
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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L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation.
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Lanzani, L., Capogna, L. & Brown, R.M. The mixed problem in L p for some two-dimensional Lipschitz domains. Math. Ann. 342, 91–124 (2008). https://doi.org/10.1007/s00208-008-0223-6
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DOI: https://doi.org/10.1007/s00208-008-0223-6