21 citations · 65 across the 12 of their papers we have counts for
13 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…
Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail
Haïm Brezis, Jean Van Schaftingen, Po-Lam Yung
In the cases where there is no Sobolev-type or Gagliardo-Nirenberg-type fractional estimate involving , we establish alternative estimates where the stron…
-convergence of non-local, non-convex functionals in one dimension
Haim Brezis, Hoai-Minh Nguyen
We study the -convergence of a family of non-local, non-convex functionals in for , where is an open interval. We show that the limit is a multiple of the…
Radial extensions in fractional Sobolev spaces
Haim Brezis, Petru Mironescu, Itai Shafrir
Given , consider its radial extension , . In "On some questions of topology fo…
Non-local functionals related to the total variation and connections with Image Processing
Haim Brezis, Hoai-Minh Nguyen
We present new results concerning the approximation of the total variation, , of a function by non-local, non-convex functionals of the form $$ Λ_δu = \int_Ω…
The BBM formula revisited
Haim Brezis, Hoai-Minh Nguyen
In this paper, we revise the BBM formula due to J. Bourgain, H. Brezis, and P. Mironescu in [1].
Distances between homotopy classes of
Haim Brezis, Petru Mironescu, Itai Shafrir
We introduce an equivalence relation on involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdo…
Distances between classes in
Haim Brezis, Petru Mironescu, Itai Shafrir
We introduce an equivalence relation on the space which classifies maps according to their "topological singularities". We establish sharp bounds for the…
Density in
Haïm Brezis, Petru Mironescu
Let be a smooth bounded domain in , $0\textless{}s\textless{}\infty$ and $1\le p\textless{}\infty$. We prove that is den…
On the optimality of shape and data representation in the spectral domain
Yonathan Aflalo, Haim Brezis, Ron Kimmel
A proof of the optimality of the eigenfunctions of the Laplace-Beltrami operator (LBO) in representing smooth functions on surfaces is provided and adapted to the field of applied…
BMO-type norms related to the perimeter of sets
Luigi Ambrosio, Jean Bourgain, Haim Brezis +1
In this paper we consider an isotropic variant of the -type norm recently introduced by Bourgain, Brezis and Mironescu. We prove that, when considering characteristic function…
Kato's inequality when is a measure
Haïm Brezis, Augusto C. Ponce
We extend the classical Kato's inequality in order to allow functions such that is a Radon measure. This inequality has been applied by Brezis, Marcus…