Nonlinear Elliptic Systems with Critical Growth - Cassani, Daniele
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The dissertation delas with existence and nonexistence results for a class of nonlinear elliptic systems which arise in looking for solitary waves in coupling the matter field with the electromagnetic field when the nonlinearity exhibits some critical behaviour; in particular this is the case of solitons which are in equilibrium with their own electromagnetic field. In the second part of the dissertation, the author develop a technique to characterize, in a variational framework, the ground state energy level of a large class of critical Hamiltonian elliptic systems.

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Produktbeschreibung
The dissertation delas with existence and nonexistence results for a class of nonlinear elliptic systems which arise in looking for solitary waves in coupling the matter field with the electromagnetic field when the nonlinearity exhibits some critical behaviour; in particular this is the case of solitons which are in equilibrium with their own electromagnetic field. In the second part of the dissertation, the author develop a technique to characterize, in a variational framework, the ground state energy level of a large class of critical Hamiltonian elliptic systems.
Autorenporträt
obtained his PhD in pure mathematics in 2006 under the guidance of Prof. Bernhard Ruf. His field of research concerns Partial Differential Equations and applications, in particular: elliptic systems, higher order nonlocal PDE with singular nonlinearities and applications to nanotechnologies, best constants in borderline inequalities.