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4 papers · 2 filters
An approximation of the squared Wasserstein distance and an application to Hamilton-Jacobi equations
Charles Bertucci, Pierre Louis Lions
We provide a simple approximation of the squared Wasserstein distance on R^d when one of the two measures is fixed. This approximation converges locally uniformly. More i…
A charged liquid drop model with Willmore energy
Michael Goldman, Matteo Novaga, Berardo Ruffini
We consider a variational model of electrified liquid drops, involving competition between surface tension and charge repulsion. Since the natural model happens to be ill-posed, we…
A spectral dominance approach to large random matrices: part II
Charles Bertucci, Jean-Michel Lasry, Pierre Louis Lions
This paper is the second of a series devoted to the study of the dynamics of the spectrum of large random matrices. We study general extensions of the partial differential equation…
A two spaces extension of Cauchy-Lipschitz Theorem
Charles Bertucci, Pierre Louis Lions
We adapt the classical theory of local well-posedness of evolution problems to cases in which the nonlinearity can be accurately quantified by two different norms. For ordinary dif…