On Strongly Exposing Functionals

On Exposed Points of the Range of a Vector Measure. Ii

If a weakly compact convex set K in a real Banach space X is strongly exposed by a dense set of functionals in X', it is proved that the functionals which expose K form a residual set in A". If v. & -* X is a measure, it follows that the set of exposing functionals of its range is a residual Gs in A". This, in turn, is found to be equivalent to a theorem of B. Walsh on the residuality of functi...

OPTIMAL TRANSPORT AND THE GEOMETRY OF LpRq

A classical theorem due to R. Phelps states that if C is a weakly compact set in a Banach space E, the strongly exposing functionals form a dense subset of the dual space E. In this paper, we look at the concrete situation where C € L1pRdq is the closed convex hull of the set of random variables Y P L1pRdq having a given law ν. Using the theory of optimal transport, we show that every random va...

Existence of infinitely many solutions for coupled system of Schrödinger-Maxwell's equations

Photoacoustic imaging in attenuating acoustic media based on strongly causal models

In this paper we derive time reversal imaging functionals for two strongly causal acoustic attenuation models, which have been proposed recently. The time reversal techniques are based on recently proposed ideas of Ammari et al for the thermo-viscous wave equation. Here and there an asymptotic analysis provides reconstruction functionals from first order corrections for the attenuating effect. ...

Critical Point Theorems concerning Strongly Indefinite Functionals and Applications to Hamiltonian Systems

Let X be a Finsler manifold. We prove some abstract results on the existence of critical points for strongly indefinite functionals f ∈ C1(X ,R) via a new deformation theorem. Different from the works in the literature, the new deformation theorem is constructed under a new version of Cerami-type condition instead of Palais-Smale condition. As applications, we prove the existence of multiple pe...