caa a22 4500 605515506 CHVBK 20210128100709.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s00205-014-0828-8 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0828-8 On the Dirichlet Problem of Mixed Type for Lower Hybrid Waves in Axisymmetric Cold Plasmas [Elektronische Daten] [Daniela Lupo, Dario Monticelli, Kevin Payne] For a class of linear second order partial differential equations of mixed elliptic-hyperbolic type, which includes a well known model for analyzing possible heating in axisymmetric cold plasmas, we give results on the weak well-posedness of the Dirichlet problem and show that such solutions are characterized by a variational principle. The weak solutions are shown to be saddle points of natural functionals suggested by the divergence form of the PDEs. Moreover, the natural domains of the functionals are the weighted Sobolev spaces to which the solutions belong. In addition, all critical levels will be characterized in terms of global extrema of the functionals restricted to suitable infinite dimensional linear subspaces. These subspaces are defined in terms of a robust spectral theory with weights which is associated to the linear operator and is developed herein. Similar characterizations for the weighted eigenvalue problem and nonlinear variants will also be given. Finally, topological methods are employed to obtain existence results for nonlinear problems including perturbations in the gradient which are then applied to the well-posedness of the linear problem with lower order terms. Springer-Verlag Berlin Heidelberg, 2014 Lupo Daniela Dipartimento di Matematica "F. Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy aut Monticelli Dario Dipartimento di Matematica "F. Enriques”, Università di Milano, Via C. Saldini 50, 20133, Milan, Italy aut Payne Kevin Dipartimento di Matematica "F. Enriques”, Università di Milano, Via C. Saldini 50, 20133, Milan, Italy aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/1(2015-07-01), 37-69 0003-9527 217:1<37 2015 217 205 https://doi.org/10.1007/s00205-014-0828-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0828-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lupo Daniela Dipartimento di Matematica "F. Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milan, Italy aut NATIONALLICENCE 700 1- Monticelli Dario Dipartimento di Matematica "F. Enriques”, Università di Milano, Via C. Saldini 50, 20133, Milan, Italy aut NATIONALLICENCE 700 1- Payne Kevin Dipartimento di Matematica "F. Enriques”, Università di Milano, Via C. Saldini 50, 20133, Milan, Italy aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/1(2015-07-01), 37-69 0003-9527 217:1<37 2015 217 205