7 papers
Equi-integrable approximation of Sobolev mappings between manifolds
Jean Van Schaftingen
We show that limits of sequences of smooth maps between compact Riemannian manifolds with equi-integrable -Sobolev energy can always be strongly approximated by smooth ma…
Morrey--Sobolev inequalities with power weights on the half-space
Jean Van Schaftingen, Leon Winter
Morrey--Sobolev inequalities are established for functions in weighted Sobolev spaces on the -dimensional half-space, where the weight is a power of the distance to the boundary…
Heterotopic energy for Sobolev mappings
Antoine Detaille, Jean Van Schaftingen
We study the notion of heterotopic energy defined as the limit of Sobolev energies of Sobolev mappings in a given homotopy class approximating almost everywhere a given Sobolev map…
Trace conjunction inequalities
Jean Van Schaftingen
Trace conjunction integrals are introduced and studied. They appear in trace conjunction inequalities which unify the Hardy inequality on a halfspace and the classical Gagliardo tr…
Extensions of traces for Sobolev mappings into manifolds at the endpoint
Jean Van Schaftingen, Benoît Van Vaerenbergh
We give direct proofs and constructions of the trace and extension theorems for Sobolev mappings in , where is Riemannian manifold with compact boundary $\part…
Generic topological screening and approximation of Sobolev maps
Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen
This manuscript develops a framework for the strong approximation of Sobolev maps with values in compact manifolds, emphasizing the interplay between local and global topological p…
Limiting Korn-Maxwell-Sobolev inequalities for general incompatibilities
Franz Gmeineder, Peter Lewintan, Jean Van Schaftingen
We give sharp conditions for the limiting Korn-Maxwell-Sobolev inequalities \begin{align*} \lVert P\rVert_{\dot{W}{^{k-1,\frac{n}{n-1}}}(\mathbb{R}^n)}\le c\big(\lVert\mathscr{A}[P…