Regularity and Well Posedness for the Laplace Operator on Polyhedral Domains
نویسنده
چکیده
We announce a well-posedness result for the Laplace equation in weighted Sobolev spaces on polyhedral domains in Rn with Dirichlet boundary conditions. The weight is the distance to the set of singular boundary points. We give a detailed sketch of the proof in three dimensions.
منابع مشابه
Regularity and Well Posedness for the Laplace Operator on Polyhedral Domains
We announce a well-posedness result for the Laplace equation in weighted Sobolev spaces on polyhedral domains in R with Dirichlet boundary conditions. The weight is the distance to the set of singular boundary points. We give a detailed sketch of the proof in three dimensions.
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 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 کاملWell-posedness, Regularity, and Finite Element Analysis for the Axisymmetric Laplace Operator on Polygonal Domains
Let L := −r−2(r∂r)2 − ∂2 z . We consider the equation Lu = f on a bounded polygonal domain with suitable boundary conditions, derived from the three-dimensional axisymmetric Poisson’s equation. We establish the well-posedness, regularity and Fredholm results in weighted Sobolev spaces, for possible singular solutions caused by the singular coefficient of the operator L, as r → 0, and by non-smo...
متن کاملBoundary Value Problems and Regularity on Polyhedral Domains
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.
متن کامل