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Approximation in Sobolev spaces by piecewise affine interpolation
Jean Van Schaftingen
Functions in a Sobolev space are approximated directly by piecewise affine interpolation in the norm of the space. The proof is based on estimates for interpolations and does not r…
Intrinsic weak derivatives and Sobolev spaces between manifolds
Alexandra Convent, Jean Van Schaftingen
We define the notion of colocally weakly differentiable maps from a manifold to a manifold . If and and are endowed with a Riemannian metric, this allows u…
Strong approximation of fractional Sobolev maps
Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen
Brezis and Mironescu have announced several years ago that for a compact manifold and for real numbers and the class $C^\i…
Interpolation inequalities between Sobolev and Morrey-Campanato spaces: A common gateway to concentration-compactness and Gagliardo-Nirenberg interpolation inequalities
Jean Van Schaftingen
We prove interpolation estimates between Morrey-Campanato spaces and Sobolev spaces. These estimates give in particular concentration-compactness inequalities in the translation-in…
Hardy-Sobolev inequalities for vector fields and canceling linear differential operators
Pierre Bousquet, Jean Van Schaftingen
Given a homogeneous k-th order differential operator on between two finite dimensional spaces, we establish the Hardy inequality $$\int_{\mathbb{R}^n} \frac{…