arXiv subjects

Emmanuel Hebey

Publications and source records attributed to Emmanuel Hebey.

8 recordsLinked to original sources

arXiv2011

Asymptotic analysis for fourth order Paneitz equations with critical growth

We investigate fourth order Paneitz equations of critical growth in the case of $n$-dimensional closed conformally flat manifolds, $n \ge 5$. Such equations arise from conformal geometry and are modelized on the Einstein case of the geometric equation describing the effects of conformal changes of metrics on the $Q$-curvature. We obtain sharp asymptotics for arbitrary bounded energy sequences of solutions of our equations from which we derive stability and compactness properties. In doing so we establish the criticality of the geometric equation with respect to the trace of its second order terms.

math.AP↗

arXiv2010

Static Klein-Gordon-Maxwell-Proca systems in 4-dimensional closed manifolds

Static Klein-Gordon-Maxwell-Proca systems are massive versions of the electrostatic Klein-Gordon-Maxwell Systems. The vector field in these systems inherits a mass and is governed by the Proca action which generalizes that of Maxwell. Following previous work by Druet & al. we prove existence and uniform bounds for such systems in the double critical case of dimension 4.

math.AP↗

arXiv2010

Existence and a priori bounds for electrostatic Klein-Gordon-Maxwell systems in fully inhomogeneous spaces

We prove existence and uniform bounds for electrostatic Klein-Gordon-Maxwell systems in the inhomogeneous context of a compact Riemannian manifold when the mass potential, balanced by the phase, is small in a quantified sense.

math.AP↗

arXiv2007

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 equation for the Einstein-scalar field system in general relativity. Our analysis introduces variational techniques, in the form of the mountain pass lemma, to the analysis of the Hamiltonian constraint equation, which has been previously studied by other methods.

gr-qc↗

arXiv2005

Critical Elliptic Systems in Potential Form

We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.

math.AP↗

arXiv2005

Sharp Sobolev Inequalities for Vector Valued Maps

We discuss sharp Sobolev inequalities for vector valued maps.

math.AP↗

arXiv2005

Stability and Perturbations of the Domain for the First Eigenvalue of the 1-Laplacian

We discuss stability of the first eigenvalue of the 1-Laplacian under perturbations of the domain.

math.AP↗

arXiv2002

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

In this paper we study the energy function associated to fourth order equations of critical growth on smooth compact conformally flat manifolds of dimension greater or equal than 5.

math.AP↗