Existence and regularity of solutions to quasilinear systems of Maxwell type and Maxwell-Stokes type

DOI10.1007/s00526-016-1081-9zbMath1362.35294OpenAlexW2547028641MaRDI QIDQ514261

Xing-Bin Pan

Publication date: 1 March 2017

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-016-1081-9

zbMATH Keywords

Dirichlet problemNeumann problemquasilinear systemsMaxwell typeMaxwell-Stokes typenonlinear partial differential systems

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with optics and electromagnetic theory (35Q60) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Weak solutions to PDEs (35D30) Electro- and magnetostatics (78A30) Semilinear elliptic equations (35J61) Quasilinear elliptic equations (35J62) Maxwell equations (35Q61)

Related Items (15)

Equivalent Relations with the J. L. Lions Lemma in a Variable Exponent Sobolev Space and Their Applications ⋮ Div-curl system with potential and Maxwell-Stokes system with natural boundary condition ⋮ Maxwell-Stokes system with Robin boundary condition ⋮ Eigenvalue problems for \(p\)-div-curl systems ⋮ Static and evolution equations with degenerate curls ⋮ The general magneto-static model and Maxwell-Stokes system with topological parameters ⋮ Maxwell-Stokes system with \(L^2\) boundary data and div-curl system with potential ⋮ On the de Rham theorem and an application to the Maxwell-Stokes type problem ⋮ Harmonic fields and Maxwell equations on perforated domains ⋮ Meissner states of type II superconductors ⋮ On a version of the de Rham theorem and an application to the Maxwell-Stokes type problem ⋮ Applications of a version of the de Rham lemma to the existence theory of a weak solution to the Maxwell-Stokes type equation ⋮ Variational and operator methods for Maxwell-Stokes system ⋮ Existence and \(W^{1,p}\) estimates of certain Maxwell type equations in Reifenberg domains ⋮ Well-posedness theory for electromagnetic obstacle problems

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