179 citations · 399 across the 5 of their papers we have counts for
5 papers
Sobolev spaces revisited
Haim Brezis, Andreas Seeger, Jean Van Schaftingen +1
We describe a recent, one-parameter family of characterizations of Sobolev and BV functions on , using sizes of superlevel sets of suitable difference quotients. This…
Families of functionals representing Sobolev norms
Haim Brezis, Andreas Seeger, Jean Van Schaftingen +1
We obtain new characterizations of the Sobolev spaces and the bounded variation space . The characterizations are in terms of t…
Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian
Soeren Fournais, Loïc Le Treust, Nicolas Raymond +1
This paper is devoted to the asymptotic analysis of the optimal Sobolev constants in the semiclassical limit and in any dimension. We combine semiclassical arguments and concentrat…
Limiting Bourgain-Brezis estimates for systems: theme and variations
Jean Van Schaftingen
J. Bourgain and H. Brezis have obtained in 2002 some new and surprising estimates for systems of linear differential equations, dealing with the endpoint case of sin…
Semi-classical states for the Choquard equation
Vital Moroz, Jean Van Schaftingen
We study the nonlocal equation $$-\varepsilon^2 Δu_\varepsilon + V u_\varepsilon = \varepsilon^{-α} \bigl(I_α\ast \lvert u_\varepsilon\rvert^p\bigr) \lvert u_\varepsilon \rvert^{p…