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…
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…
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…
Analytical obstructions to the weak approximation of Sobolev mappings into manifolds
Antoine Detaille, Jean Van Schaftingen
For any integer , we construct a compact Riemannian manifold such that if , there is a map in the Sobolev space of mappings $ W^…
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…