The Poisson and Stokes problems on weighted spaces in Lipschitz domains and under singular forcing

DOI10.1016/j.jmaa.2018.10.094zbMath1404.35122OpenAlexW2900096382WikidataQ128969051 ScholiaQ128969051MaRDI QIDQ1633579

Enrique Otárola, Abner J. Salgado

Publication date: 20 December 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.10.094

zbMATH Keywords

Poisson equationLipschitz domainsStokes equation

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (12)

On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra ⋮ An optimal control problem for the Navier-Stokes equations with point sources ⋮ A Posteriori Error Estimates for the Stationary Navier--Stokes Equations with Dirac Measures ⋮ Error estimates for optimal control problems involving the Stokes system and Dirac measures ⋮ A posteriori error estimates for the Stokes problem with singular sources ⋮ The stationary Boussinesq problem under singular forcing ⋮ Error estimates in weighted Sobolev norms for finite element immersed interface methods ⋮ A weighted setting for the stationary Navier Stokes equations under singular forcing ⋮ Optimal a priori error estimates in weighted Sobolev spaces for the Poisson problem with singular sources ⋮ Stability of the Stokes projection on weighted spaces and applications ⋮ A Weighted Setting for the Numerical Approximation of the Poisson Problem with Singular Sources ⋮ An Adaptive FEM for the Pointwise Tracking Optimal Control Problem of the Stokes Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Powers of distances to lower dimensional sets as Muckenhoupt weights
• Existence, uniqueness and optimal regularity results for very weak solutions to nonlinear elliptic systems
• Piecewise polynomial interpolation in Muckenhoupt weighted Sobolev spaces and applications
• Weighted \(L^q\)-theory for the Stokes resolvent in exterior domains
• Nonlinear potential theory and weighted Sobolev spaces
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Finite Element Approximation of Elliptic Problems with Dirac Measure Terms in Weighted Spaces: Applications to One- and Three-dimensional Coupled Problems
• A posteriorierror estimates for elliptic problems with Dirac measure terms in weighted spaces
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• A Unified Theory for Some Non-Newtonian Fluids Under Singular Forcing
• Weighted Sobolev spaces and embedding theorems
• Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
• Weighted Norm Inequalities for the Hardy Maximal Function

This page was built for publication: The Poisson and Stokes problems on weighted spaces in Lipschitz domains and under singular forcing