17 citations · 26 across the 11 of their papers we have counts for
6 papers · 1 filter
Maximizing one Laplace eigenvalue on n-dimensional manifolds
Romain Petrides
We prove existence and regularity results for the problem of maximization of one Laplace eigenvalue with respect to metrics of same volume lying in a conformal class of a Riemannia…
A variational method for functionals depending on eigenvalues
Romain Petrides
We perform a systematic variational method for functionals depending on eigenvalues of Riemannian manifolds. It is based on a new concept of Palais Smale sequences that can be cons…
Existence of Ginzburg-Landau minimizers with optimal boundary data and applications
PAul Laurain, Romain Petrides
We perform the classical Ginzburg-Landau analysis originated from the celebrated paper by Bethuel, Brezis, Hélein for optimal boundary data. More precisely, we give optimal regular…
Regularity and quantification for harmonic maps with free boundary
Paul Laurain, Romain Petrides
We prove a quantification result for harmonic maps with free boundary from arbitrary Riemannian surfaces into the unit ball of with bounded energy. This general…
Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces
Romain Petrides
We investigate in this paper the existence of a metric which maximizes the first eigenvalue of the Laplacian on Riemannian surfaces. We first prove that, in a given conformal class…
On a rigidity result for the first conformal eigenvalue of the Laplacian
Romain Petrides
Given a smooth compact Riemannian manifold without boundary of dimension , we consider the first conformal eigenvalue which is by definition the supremum of the fi…