21 Result(s)

Article

Strong convergence of the Bopp–Podolsky–Schrödinger–Proca system to the Schrödinger–Poisson–Proca system in the electro-magneto-static case

We prove strong convergence of the Bopp–Podolsky–Schrödinger–Proca system to the Schrödinger–Poisson–Proca system in the electro-magneto-static case as the Bopp–Podolsky parameter goes to zero.

Emmanuel Hebey in Calculus of Variations and Partial Differential Equations (2020)

Article

Klein–Gordon–Maxwell–Proca type systems in the electro-magneto-static case: the high dimensional case

We investigate Klein–Gordon–Maxwell–Proca type systems in the context of closed n-dimensional manifolds with \(n \ge 4\) ...

Emmanuel Hebey, Pierre-Damien Thizy in Calculus of Variations and Partial Differe… (2019)

Article

Stationary Kirchhoff systems in closed \(3\) -dimensional manifolds

We discuss existence of solutions, compactness and uniqueness properties for Kirchhoff type systems in closed \(3\)

Emmanuel Hebey, Pierre-Damien Thizy in Calculus of Variations and Partial Differe… (2015)

Article

Schrödinger–Poisson systems in the 3-sphere

We investigate nonlinear Schrödinger–Poisson systems in the 3-sphere. We prove existence results for these systems and discuss the question of the stability of the systems with respect to their phases. While, ...

Emmanuel Hebey, Juncheng Wei in Calculus of Variations and Partial Differential Equations (2013)

Article

Stability and instability for Einstein-scalar field Lichnerowicz equations on compact Riemannian manifolds

We investigate stability issues for Einstein-scalar field Lichnerowicz equations in the inhomogeneous context of a compact Riemannian manifold. We prove that stability holds true when the dimension n is such that...

Olivier Druet, Emmanuel Hebey in Mathematische Zeitschrift (2009)

Article

A Variational Analysis of Einstein–Scalar Field Lichnerowicz Equations on Compact Riemannian Manifolds

We establish new existence and non-existence results for positive solutions of the Einstein–scalar field Lichnerowicz equation on compact manifolds. This equation arises from the Hamiltonian constraint equatio...

Emmanuel Hebey, Frank Pacard, Daniel Pollack in Communications in Mathematical Physics (2008)

Article

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

Let (M, g) be a smooth compact Riemannian n-manifold, n ≥ 3. Let also p ≥ 1 be an integer, and \(M_p^s(\mathbb {R})\)

Olivier Druet, Emmanuel Hebey in Calculus of Variations and Partial Differential Equations (2008)

Article

Sharp Sobolev inequalities for vector valued maps

Emmanuel Hebey in Mathematische Zeitschrift (2006)

Article

Stability and perturbations of the domain for the first eigenvalue of the 1-Laplacian

We study the dependence of the first eigenvalue of the 1-Laplacian with respect to perturbations of the domain. We provide results ranging from general type of perturbations to regular perturbations by diffeom...

Emmanuel Hebey, Nicolas Saintier in Archiv der Mathematik (2006)

Article

Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case

Given (M,g) a smooth compact Riemannian manifold of dimension n ≥ 5, we consider equations like $$P_{g} u = u^{{2^{\# } - 1}} ,$$ ...

Veronica Felli, Emmanuel Hebey… in Nonlinear Differential Equations and Appli… (2005)

Chapter and Conference Paper

Bubbles over Bubbles: A C ⁰-theory for the Blow-up of Second Order Elliptic Equations of Critical Sobolev Growth

Let (M, g,) be a smooth compact Riemannian manifold of dimension n ≥ 3, and △ ^g =-div ^g ▽ be the Laplace-Beltrami operator. Let also 2^* be the c...

Emmanuel Hebey in Variational Problems in Riemannian Geometry (2004)

Article

Sharp Sobolev inequalities of second order

Let (M, g) be a smooth compact Riemannian manifold of dimension n≥5, and ₂ ² (M) be the Sobolev space consisting of functions in L²(M) whose derivatives up to ...

Emmanuel Hebey in The Journal of Geometric Analysis (2003)

Article

Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients

Emmanuel Hebey… in Calculus of Variations and Partial Differential Equations (2001)

Article

From best constants to critical functions

The study of sharp Sobolev inequalities starts with the notion of best constant and leads naturally to the question to know whether or not there exist extremal functions for these inequalities. We restrict ou...

Emmanuel Hebey, Michel Vaugon in Mathematische Zeitschrift (2001)

Article

EffectiveL _p pinching for the concircular curvature

According to the work of Huisken, Margerin, and Nishikawa, we know that effective L_∞ pinching assumptions on the concircular curvature lead to the existence of a metric of constant positive sectional curvature. B...

Emmanuel Hebey, Michel Vaugon in The Journal of Geometric Analysis (1996)

Chapter

Sobolev spaces

Emmanuel Hebey in Sobolev Spaces on Riemannian Manifolds (1996)

Chapter

Geometric preliminaries

Emmanuel Hebey in Sobolev Spaces on Riemannian Manifolds (1996)

Chapter

Sobolev spaces in the presence of symmetries

Emmanuel Hebey in Sobolev Spaces on Riemannian Manifolds (1996)

Chapter

The best constants problems

Emmanuel Hebey in Sobolev Spaces on Riemannian Manifolds (1996)