Interface and mixed boundary value problems on $n$-dimensional polyhedral domains
By Constantin Bacuta, A. Mazzucato, Victor Nistor, Ludmil T. Zikatanov. Documenta Mathematica, 2010
62 citations recorded by the source corpus.
Let � 2 Z+ be arbitrary. We prove a well-posedness result for mixed boundary value/interface problems of second-order, positive, strongly elliptic operators in weighted Sobolev spaces K �() on a bounded, curvilinear polyhedral domain in a manifold M of dimension n. The typical weightthat we consider is the (smoothed) distance to the set of singular boundary points of @. Our model problem is Pu := −div(Ar u) = f, in , u = 0 on @D, and D P � u = 0 on @�, where the function A � � >0 is piece-wise smooth on the polyhedral decomposition ¯ = ( jj, and @ = @D ( @N is a decomposition of the boundary into polyhedral subsets corre- sponding, respectively, to Dirichlet and Neumann boundary condi- tions. If there are no interfaces and no adjacent faces with Neu- mann boundary conditions, our main result gives an isomorphism P : K �+1
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/a23756353c177ac15a38833c9eac827f394d02d7
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In Applied Mathematics
- Hengguang Li
- Victor Nistor
- A. Mazzucato
- Yoshihiro Sawano
- Kwok-Pun Ho
- Hitoshi Tanaka
- Giuseppe Mingione
- Martin Dindos
In Computational Theory and Mathematics
Citations in the corpus
- Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks (2010, methodology): “The desingularization Σ D was used already in the framework of manifolds with corners by Melrose [67]. See also [3,4, 14 ].”
- ANALYSIS OF THE FINITE ELEMENT METHOD FOR TRANSMISSION/MIXED BOUNDARY VALUE PROBLEMS ON GENERAL POLYGONAL DOMAINS ∗ (2010, background): “3 extend to 3D (see [58] for proofs in the absence of interfaces and [16] for a proof of the regularity in the presence of interfaces in n-dimensions).”