Divergence operator and Poincaré inequalities on arbitrary bounded domains

DOI10.1080/17476931003786659zbMath1205.35044arXiv0906.2050OpenAlexW2038611583MaRDI QIDQ4931833

Ricardo G. Durán, Emmanuel Russ, María Amelia Muschietti, Philippe Tchamitchian

Publication date: 1 October 2010

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.2050

zbMATH Keywords

\(s\)-John domainsright invertibilityweighted Lebesgue and Sobolev spaces

Mathematics Subject Classification ID

Boundary value problems for linear first-order PDEs (35F15) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (16)

A hybrid high-order method for creeping flows of non-Newtonian fluids ⋮ Improved Poincar\'e inequalities in fractional Sobolev spaces ⋮ Korn's inequalities for generalized external cusps ⋮ Improved weighted Poincaré inequalities in John domains and application to the divergence equation ⋮ Construction of a right inverse for the divergence in non-cylindrical time dependent domains ⋮ Weighted discrete Hardy inequalities on trees and applications ⋮ Solvability of the divergence equation implies John via Poincaré inequality ⋮ Korn inequality on irregular domains ⋮ A decomposition technique for integrable functions with applications to the divergence problem ⋮ Hardy and Hardy-Sobolev spaces on strongly Lipschitz domains and some applications ⋮ Korn inequality and divergence operator: Counterexamples and optimality of weighted estimates ⋮ Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method ⋮ Removable singularities for div v=f in weighted Lebesgue spaces ⋮ Degenerate Poincaré–Sobolev inequalities ⋮ Solvability in weighted Lebesgue spaces of the divergence equation with measure data ⋮ On the inequalities of Babuška-Aziz, Friedrichs and Horgan-Payne

Cites Work

• Hardy Sobolev spaces on strongly Lipschitz domains of \(\mathbb R^n\)
• Solutions of the divergence operator on John domains
• Improved Poincaré inequalities with weights
• Lipschitz maps and nets in Euclidean space
• An explicit right inverse of the divergence operator which is continuous in weighted norms
• A decomposition technique for John domains
• On the equation 𝑑𝑖𝑣𝑌=𝑓 and application to control of phases
• SOLUTIONS OF THE DIVERGENCE AND ANALYSIS OF THE STOKES EQUATIONS IN PLANAR HÖLDER-α DOMAINS

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