We bound the number of electrons \( Q \) that an atom can bind in excess of neutrality for density functionals generalizing the classical Thomas-Fermi-Weizsäcker functional: instead of the classical ...
For a Riemann surface X and a complex reductive group G, G-character varieties are moduli spaces parametrizing G-local systems on X. When G=GLn, the cohomology of these character varieties have been ...
We are interested here in questions related to the study of some divergence elliptic equations in bounded Lipschitz or \( C^1 \) domains: \( div (a\nabla u) + bu = f\quad in\,\,\Omega, \) with Diric...
The regularity of solutions of the Dirichlet problem for the Laplace operator in corner domains is limited by the existence of harmonic functions that are zero on the boundary of some tangent cones. T...
On non-smooth domains, elliptic regularity for solutions of boundary value problems, measured by Sobolev norms, will only hold for a restricted set of regularity indices, due to singularities of the s...
- Abstract: In the first part of the course we will provide a brief introduction to the spectrum of the Laplacian on Euclidean domains and Riemannian manifolds, along with a few basic examples, and th...
The development of efficient reduced order models (ROMs) from a deep learning perspective enables users to overcome the limitations of traditional approaches. One drawback of the techniques based on c...
