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4 papers · 2 filters
On the dependence of the nonlinear Schrodinger flow upon the power of the nonlinearity
Rémi Carles, Quentin Chauleur, Guillaume Ferriere
We prove continuity properties for the flow map associated to the defocusing energy-subcritical power-like nonlinear Schr{ö}dinger equation, when the power varies. We show local in…
Least-energy solutions of the Brézis-Nirenberg problem in the non-coercive case in dimension
Hussein Cheikh Ali, Bruno Premoselli
Let be a bounded, smooth domain of and . We consider the celebrated Brézis-Nirenberg problem: \begin{equation}\label{eq:critlambda:abs} \tag{*}…
Compactness for the Hardy-Sobolev equation on manifolds
Hussein Cheikh Ali, Saikat Mazumdar
Let be a closed Riemannian manifold of dimension , and let be such that the operator is coercive. Fix and . We…
A ill-posed scattering problem saturating Weyl's law
T. Chaumont-Frelet
This paper focuses on the well-posedness (or lack thereof) of three-dimensional time-harmonic wave propagation problems modeled by the Helmholtz equation. It is well-known that if…