Boundary Value Problems and Regularity on Polyhedral Domains
نویسندگان
چکیده
We prove a well-posedness result for second order boundary value problems in weighted Sobolev spaces on curvilinear polyhedral domains in Rn with Dirichlet boundary conditions. Our typical weight is the distance to the set of singular boundary points.
منابع مشابه
Weighted analytic regularity in polyhedra
We explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems. The abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors’ paper in Math. Models Methods Appl. Sci. 22 (8) (2012). We illustrate this strategy by considering problems set in smooth domains...
متن کاملAnisotropic regularity and optimal rates of convergence on three dimensional polyhedral domains
We consider the the Poisson problem −∆u = f ∈ Ω, u = g on ∂Ω, where Ω is a bounded domain in R. The objective of the paper is twofold. The first objective is to present the well posedness and the regularity of the problem using appropriate weighted spaces for the data and the solution. The second objective is to illustrate how weighted regularity results for the Laplace operator are used in des...
متن کاملSobolev Spaces and Regularity for Polyhedral Domains
We prove a regularity result on polyhedral domains P ⊂ R using the weighted Sobolev spaces Ka (P). In particular, we show that there is no loss of Ka –regularity for solutions of strongly elliptic systems with smooth coefficients. In the proof, we identify Ka (P) with the Sobolev spaces on P associated to the metric r P gE , where gE is the Euclidean metric and rP(x) is a smoothing of the Eucli...
متن کاملAnisotropic Regularity and Optimal Rates of Convergence for the Finite Element Method on Three Dimensional Polyhedral Domains
We consider the model Poisson problem −∆u = f ∈ Ω, u = g on ∂Ω, where Ω is a bounded polyhedral domain in Rn. The objective of the paper is twofold. The first objective is to review the well posedness and the regularity of our model problem using appropriate weighted spaces for the data and the solution. We use these results to derive the domain of the Laplace operator with zero boundary condit...
متن کاملSobolev Spaces on Lie Manifolds and Regularity for Polyhedral Domains
We study some basic analytic questions related to differential operators on Lie manifolds, which are manifolds whose large scale geometry can be described by a a Lie algebra of vector fields on a compactification. We extend to Lie manifolds several classical results on Sobolev spaces, elliptic regularity, and mapping properties of pseudodifferential operators. A tubular neighborhood theorem for...
متن کامل