Open AccessJournal Article
Interface and mixed boundary value problems on n-dimensional polyhedral domains
Reads0
Chats0
TLDR
In this paper, a well-posedness result for mixed boundary value/interface problems of second-order, positive, strongly elliptic operators in weighted Sobolev spaces was given.Abstract:
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 �+1read more
Citations
More filters
Journal ArticleDOI
Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks
Anna L. Mazzucato,Victor Nistor +1 more
TL;DR: In this article, a regularity result for the anisotropic linear elasticity equation with mixed displacement and traction boundary conditions on a curved polyhedral domain was established. But the results were not extended to other strongly elliptic systems and higher dimensions.
Journal Article
Analysis of the finite element method for transmission/mixed boundary value problems on general polygonal domains ∗
TL;DR: In this article, the authors studied the impl ementation of the finite element method for a strongly elliptic second order equation with jump discontinuities in its coefficients on a polygonal domain that may have cracks or vertices that touch the boundary.
Journal ArticleDOI
On Besov regularity of solutions to nonlinear elliptic partial differential equations
Stephan Dahlke,Winfried Sickel +1 more
TL;DR: In this paper, the authors studied the regularity of the solutions to nonlinear elliptic equations and showed that the Besov regularity is high enough to justify the use of adaptive schemes.
Journal ArticleDOI
Pseudodifferential operators on manifolds with fibred corners
TL;DR: In this paper, a pseudodifferential calculus generalizing the Phi-calculus of Mazzeo and Melrose is proposed. But it is based on the assumption that a stratified pseudomanifold can be resolved into a manifold with fibred corners.
Posted Content
Pseudodifferential operators on manifolds with fibred corners
TL;DR: In this article, a pseudodifferential calculus generalizing the Phi-calculus of Mazzeo and Melrose is proposed. But it is based on the assumption that a stratified pseudomanifold can be resolved into a manifold with fibred corners.
References
More filters
Book
Non-homogeneous boundary value problems and applications
TL;DR: In this paper, the authors consider the problem of finding solutions to elliptic boundary value problems in Spaces of Analytic Functions and of Class Mk Generalizations in the case of distributions and Ultra-Distributions.
Book
Elliptic Problems in Nonsmooth Domains
TL;DR: Second-order boundary value problems in polygons have been studied in this article for convex domains, where the second order boundary value problem can be solved in the Sobolev spaces of Holder functions.
Book
Strongly Elliptic Systems and Boundary Integral Equations
TL;DR: In this article, the Laplace equation, the Helmholtz equation, and the Sobolev spaces of strongly elliptic systems have been studied and further properties of spherical harmonics have been discussed.
Book
Introduction to partial differential equations
TL;DR: The Introduction to Partial Differential Equations (IDEQE) as discussed by the authors is the most widely used partial differential equation (PDE) formalism for algebraic partial differential equations.