Sharp Sobolev inequalities for vector valued maps

Uniqueness of ground states of some coupled nonlinear Schrödinger systems and their application

“…If one uses Hölder inequality directly, one can only get a vector-valued GagliardoNirenberg inequality like [9]. In [10], E. Hebey investigated very interesting sharp vector-valued Sobolev inequalities in the case of compact manifolds.…”

Sharp asymptotics and compactness for local low energy solutions of critical elliptic systems in potential form

“…The case of systems turns out to be more involved because of the interactions which occur between the different equations in the system. Partial answers are in Hebey [28][29][30]. We restrict ourselves in this paper in proving control by the bubbles in (1.4) and sharp asymptotics in the case the U α 's have only isolated flat blow-up points.…”

“…They have been the target of investigations for decades and are currently subject to an intensive research activity. Without any pretention to exhaustivity, we mention that possible references on elliptic systems are Amster et al [1], Angenent and Van der Vorst [2,3], Clément et al [13], De Figueiredo [14], De Figueiredo and Ding [15], De Figueiredo and Felmer [16], De Figueiredo and Sirakov [17], El Hamidi [21], Giaquinta and Martinazzi [22], Hebey [28][29][30], Hulshof et al [33], Jost et al [34], Jost and Wang [35], Mancini and Mitidieri [42], Mitidieri and Sweers [44], Montenegro [45], Pompino [47], Qing [48], and Sweers [60].…”