We prove an existence result for trajectories of classical particles accelerated by a potential and a magnetic field on a non--complete Riemannian manifold $M$. Both the potential and the magnetic field may be not bounded and have critical growth. We state a suitable convexity assumption involving the magnetic field in order to prove that the support of each trajectory is entirely contained in M.
Trajectories of a charge in a magnetic field on Riemannian manifolds with boundary / Bartolo, Rossella; Germinario, A.. - In: DYNAMICS OF CONTINUOUS, DISCRETE AND IMPULSIVE SYSTEMS. SERIES A: MATHEMATICAL ANALYSIS. - ISSN 1201-3390. - 17:3(2010), pp. 363-376.
Trajectories of a charge in a magnetic field on Riemannian manifolds with boundary
BARTOLO, Rossella;
2010-01-01
Abstract
We prove an existence result for trajectories of classical particles accelerated by a potential and a magnetic field on a non--complete Riemannian manifold $M$. Both the potential and the magnetic field may be not bounded and have critical growth. We state a suitable convexity assumption involving the magnetic field in order to prove that the support of each trajectory is entirely contained in M.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
