Andrea Malchiodi

A perturbation result for the Webster scalar curvature problem on the CR sphere

Abstract We consider the problem of prescribing the Webster scalar curvature on the unit sphere of C n+1 . Using a perturbation method, we obtain existence results for curvatures close to a positive constant and satisfying an assumption of Bahri–Coron type.

Prescribing scalar and boundary mean curvature on the three dimensional half sphere

We consider the problem of prescribing the scalar curvature and the boundary mean curvature of the standard half-three sphere, by deforming conformally its standard metric. Using blow-up analysis techniques and minimax arguments, we prove some existence and compactness results.

SOME REMARKS ON THE EQUATION FOR VARYING λ, p AND VARYING DOMAINS*

ABSTRACT We consider positive solutions of the equation with Dirichlet boundary conditions in a smooth bounded domain Ω for λ > 0 and p > 1. We study the behavior of the solutions for varying λ, p and varying domains Ω in different limiting situations. *This research was supported by MURST project “Metodi Variazionali ed Equazioni Differenziali non Lineari”. A.M. is supported by a Fulbright fellowship for the academic year 2000–2001.

Solutions concentrating on spheres to symmetric singularly perturbed problems

Abstract We discuss some existence results concerning problems (NLS) and (N), proving the existence of radial solutions concentrating on a sphere. To cite this article: A.xa0Ambrosetti et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 145–150.

Singular elliptic problems with critical growth

ABSTRACT We consider Dirichlet problems of the form in Ω, u = 0 on ∂Ω, where Ω is an arbitrary domain in , with N ≥ 3, α ∈ ε(0,2), and p = 2(N−α)/(N−2) is the corresponding critical exponent. A lack of compactness may occur when or Ω is unbounded, because of concentration phenomena at the origin or vanishing, due to dilation invariance. We study the existence of positive solutions with respect to the geometry of the domain Ω.

Curvature theory of boundary phases: the two-dimensional case

We describe the behaviour of minimum problems involving non-convex surface integrals in 2D singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted.