A -theory for the blow-up of second order elliptic equations of critical Sobolev growth.
A compactness result for polyharmonic maps in the critical dimension
For , let be a bounded smooth domain and a compact smooth Riemannian manifold without boundary. Suppose that is a sequence of weak solutions in the critical dimension to the perturbed -polyharmonic maps with in and weakly in . Then is an -polyharmonic map. In particular, the space of -polyharmonic maps is sequentially compact for the weak- topology.
A complement to the Fredholm theory of elliptic systems on bounded domains.
A discreteness criterion for the spectrum of the Laplace--Beltrami operator on quasimodel manifolds.
A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations
A geometric and analytic approach to some problems associated with Emden equations
A Lie transformation group attached to a second order elliptic operator.
A property of Sobolev spaces on complete Riemannian manifolds.
A reduction method for proving the existence of solutions to elliptic equations involving the -Laplacian.
A relationship between volume, injectivity radius, and eigenvalues.
A strong maximum principle for the Paneitz operator and a non-local flow for the -curvature
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive -curvature. Modifying the test function construction of Esposito-Robert, we show...
Almost product structures and Monge-Ampère equations.
Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds
In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according to the Weyl law, well-known in the self-adjoint case.
An upper bound for the first eigenvalue of the Dirac operator on compact spin manifolds.
Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme
Analyse sur les boules d' un opérateur sous-elliptique.
Analytic index formulas for elliptic corner operators
Spaces with corner singularities, locally modelled by cones with base spaces having conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise smooth geometry. We consider a typical case of a manifold with corners, the so-called "edged spindle", and a natural algebra of pseudodifferential operators on it with special degeneracy in the symbols, the "corner algebra". There are three levels of principal symbols in the corner algebra, namely the interior,...