Franchi, Bruno; Obrecht, Enrico; Vecchi, Eugenio On a class of semilinear evolution equations for vector potentials associated with Maxwell’s equations in Carnot groups. (English) Zbl 1284.35420 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 90, 56-69 (2013). Summary: In this paper we prove existence and regularity results for a class of semilinear evolution equations that are satisfied by vector potentials associated with Maxwell’s equations in Carnot groups (connected, simply connected, stratified nilpotent Lie groups). The natural setting for these equations is provided by the so-called Rumin’s complex of intrinsic differential forms. Cited in 3 Documents MSC: 35Q61 Maxwell equations 35R03 PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. 58A10 Differential forms in global analysis 49J45 Methods involving semicontinuity and convergence; relaxation 22E25 Nilpotent and solvable Lie groups Keywords:Carnot groups; differential forms; semilinear Maxwell’s equations PDFBibTeX XMLCite \textit{B. Franchi} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 90, 56--69 (2013; Zbl 1284.35420) Full Text: DOI References: [1] Bahouri, Hajer; Gérard, Patrick, High frequency approximation of solutions to critical nonlinear wave equations, Amer. J. Math., 121, 1, 131-175 (1999) · Zbl 0919.35089 [2] Bahouri, Hajer; Gérard, Patrick; Xu, Chao-Jiang, Espaces de Besov et estimations de Strichartz généralisées sur le groupe de Heisenberg, J. Anal. 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