Higher \(L^p\) regularity for vector fields that satisfy divergence and rotation constraints in dual Sobolev spaces, and application to some low-frequency Maxwell equations

DOI10.3934/dcdss.2015.8.475zbMath1304.35168OpenAlexW2313169952MaRDI QIDQ479107

Pierre-Étienne Druet

Publication date: 5 December 2014

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2015.8.475

zbMATH Keywords

transmission conditionsDiv-Curl inequalityDiv-Curl Lemmanonsmooth interfaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with optics and electromagnetic theory (35Q60) Maxwell equations (35Q61)

Related Items (2)

An existence result for a suspension of rigid magnetizable particles ⋮ Mosco convergence for \(H(\text{curl})\) spaces, higher integrability for Maxwell's equations, and stability in direct and inverse EM scattering problems

Cites Work

• Unnamed Item
• Unnamed Item
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• An elementary proof for a compact imbedding result in generalized electromagnetic theory
• Neumann and mixed problems on curvilinear polyhedra
• Modeling and simulation of sublimation growth of SiC bulk single crystals
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals
• Elliptic model problems including mixed boundary conditions and material heterogeneities
• Optimal regularity for elliptic transmission problems including \(C^1\) interfaces
• On a generalization of the ``div-curl lemma
• Optimal Control of Three-Dimensional State-Constrained Induction Heating Problems with Nonlocal Radiation Effects
• A model for resistance welding including phase transitions and Joule heating
• Optimal Control for the Thermistor Problem
• On the low frequency asymptotics in electromagnetic theory.
• A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
• On Weak Continuity and the Hodge Decomposition
• Estimating ∇u by divu and curlu
• Vector potentials in three-dimensional non-smooth domains
• A compactness result for vector fields with divergence and curl in L^q(ω) involving mixed boundary conditions
• The Inhomogeneous Neumann Problem in Lipschitz Domains
• Finite Element Methods for Maxwell's Equations

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