MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Existence and Regularity for an Energy Maximization Problem in Two Dimensions

Spyridon Kamvissis and Evguenii Rakhmanov


We consider the variational problem of maximizing the weighted equilibrium Green's energy of a distribution of charges free to move in a subset of the upper half-plane, under a particular external field. We show that this problem admits a solution and that, under some conditions, this solution is regular in some strictly defined sense: it is an S-curve. The above problem appears in the theory of weak dispersive limits of integrable equations. In particular, its solution provides a justification of a crucial step in the asymptotic theory of steepest descent for the associated Riemann-Hilbert problems.

semiclassical nls, maximal equilibrium energy problem, s-curve

Related publications

2005 Repository Open Access
Spyridon Kamvissis and Evguenii A. Rakhmanov

Existence and regularity for an energy maximization problem in two dimensions

In: Journal of mathematical physics, 46 (2005) 8, p. 083505