WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS

DOI10.1142/S0219199712500320zbMath1251.35175MaRDI QIDQ3166704

Maria Carla Tesi, Bruno Franchi

Publication date: 15 October 2012

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

differential formsMaxwell's equationswave equationsCarnot groups

Mathematics Subject Classification ID

Wave equation (35L05) Differential forms in global analysis (58A10) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Equations in function spaces; evolution equations (58D25) Maxwell equations (35Q61)

Related Items (10)

Gagliardo-Nirenberg inequalities for differential forms in Heisenberg groups ⋮ Intrinsic Lipschitz graphs within Carnot groups ⋮ \(\Gamma \)-convergence of variational functionals with boundary terms in Stein manifolds ⋮ Horizontal magnetic fields and improved Hardy inequalities in the Heisenberg group ⋮ An alternative construction of the Rumin complex on homogeneous nilpotent Lie groups ⋮ On a class of semilinear evolution equations for vector potentials associated with Maxwell's equations in Carnot groups ⋮ Sharp a priori estimates for div-curl systems in Heisenberg groups ⋮ Differential forms in Carnot groups: a \(\Gamma \)-convergence approach ⋮ Gagliardo-Nirenberg Inequalities for Horizontal Vector Fields in the Engel Group and in the Seven-Dimensional Quaternionic Heisenberg Group ⋮ Gaffney-Friedrichs inequality for differential forms on Heisenberg groups

Cites Work

• Faraday's form and Maxwell's equations in the Heisenberg group
• Differential forms in Carnot groups: a \(\Gamma \)-convergence approach
• Models for free nilpotent Lie algebras
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• Fundamental solution and sharp \(L^p\) estimates for Laplace operators in the contact complex of Heisenberg groups
• Quasiconformal mappings on the Heisenberg group
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Pseudodifferential operators on groups with dilations
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Differential forms on contact manifolds
• On the structure of finite perimeter sets in step 2 Carnot groups
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Compensated compactness for differential forms in Carnot groups and applications
• Local solvability and holmogeneous distributions on the heisenberg group
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie groups
• Compensated compactness in the contact complex of Heisenberg groups
• DIV–CURL TYPE THEOREM, H-CONVERGENCE AND STOKES FORMULA IN THE HEISENBERG GROUP

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