Surfaces à courbure moyenne constante et inégalité de Wente
We show that if Ω is an open subset of ℝ², then the surjectivity of a partial differential operator P(D) on the space of ultradistributions of Beurling type is equivalent to the surjectivity of P(D) on .
We analyze the problem of switching controls for control systems endowed with different actuators. The goal is to control the dynamics of the system by switching from an actuator to the other in a systematic way so that, in each instant of time, only one actuator is active. We first address a finite-dimensional model and show that, under suitable rank conditions, switching control strategies exist and can be built in a systematic way. To do this we introduce a new variational principle building...
The symbol calculus on the upper half plane is studied from the viewpoint of the Kirillov theory of orbits. The main result is the -estimates for Fuchs type pseudodifferential operators.
Si danno condizioni sufficienti e condizioni necessarie affinché il problema di Cauchy per alcuni operatori di tipo Schrödinger sia ben posto in spazi di Sobolev. Gli operatori qui considerati sono operatori di Schrödinger con potenziali vettoriali complessi, una generalizzazione degli operatori di 2-evoluzione nel senso di Petrowsky, e alcuni sistemi tipo Leray-Volevich di operatori lineari a derivate parziali. Il metodo che usiamo in questo articolo è la simmetrizazione degli operatori non dipendenti...
Symmetric hyperbolic systems with a class of non-homogeneous boundary conditions that do not satisfy the Kreiss-Sakamoto condition (or uniform Lopatinskii condition) are discussed. The boundary conditions are of conservative type. An energy estimate which provides interior and boundary regularity for weak solutions to the system is proved. The results are valid for operators with rough coefficients. As an example the anisotropic Maxwell system is considered.
The (infinitesimal) symmetries of first and second-order partial differential equations represented by connections on fibered manifolds are studied within the framework of certain “strong horizontal“ structures closely related to the equations in question. The classification and global description of the symmetries is presented by means of some natural compatible structures, eġḃy vertical prolongations of connections.
Symmetries of the defocusing nonlinear Schrödinger equation are expressed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Zakharov-Shabat system. Application: proof of the conjecture that the periodic spectrum of a Zakharov-Shabat operator is symmetric,i.e. for all , if and only if the sequence of gap lengths, , is symmetric with respect to .
In this paper, we consider shape optimization problems for the principal eigenvalues of second order uniformly elliptic operators in bounded domains of . We first recall the classical Rayleigh-Faber-Krahn problem, that is the minimization of the principal eigenvalue of the Dirichlet Laplacian in a domain with fixed Lebesgue measure. We then consider the case of the Laplacian with a bounded drift, that is the operator , for which the minimization problem is still well posed. Next, we deal with...