The Regularity Problem in Rough Subdomains of Riemannian Manifolds

M. Mitrea () and B. Schmutzler ()
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M. Mitrea: University of Missouri
B. Schmutzler: University of Missouri

Chapter Chapter 36 in Integral Methods in Science and Engineering, 2015, pp 427-440 from Springer

Abstract: Abstract Let ℳ $$\mathcal{M}$$ be a Riemannian manifold and suppose Ω ⊂ ℳ $$\varOmega \subset \mathcal{M}$$ is a regular SKT domain. In this setting, we prove the well-posedness of the Regularity boundary value problem for the Laplace–Beltrami operator associated with the metric on ℳ $$\mathcal{M}$$ , with boundary data from the L p -based Sobolev space of order one on ∂ Ω. This is achieved using potential theoretic methods and complements work in [HoMiTa10], where the Dirichlet problem has been treated.

Keywords: Dirichlet Boundary Value Problem; Laplace–Beltrami Operator; Boundary Layer Potentials; Nontangential Maximal Function; Regularity Boundary Value Problem; Regular SKT Domain; Riemannian Manifold (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-16727-5_36

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