8 citations · 8 across the 2 of their papers we have counts for
5 papers · 1 filter
An estimate of the Hopf degree of fractional Sobolev mappings
Armin Schikorra, Jean Van Schaftingen
We estimate the Hopf degree for smooth maps from to in the fractional Sobolev space. Namely we show that for …
Metric characterization of the sum of fractional Sobolev spaces
Rémy Rodiac, Jean Van Schaftingen
We introduce a non-linear criterion which allows us to determine when a function can be written as a sum of functions belonging to homogeneous fractional spaces: for $\ell \in \mat…
Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo's lemma
Daniel Spector, Jean Van Schaftingen
We prove a family of Sobolev inequalities of the form where $A (D) : C^\i…
Sobolev mappings: from liquid crystals to irrigation via degree theory
Jean Van Schaftingen
Sobolev spaces are a natural framework for the analysis of problems in partial differential equations and calculus of variations. Some physical and geometric contexts, such as liqu…
Nonlocal Hardy type inequalities with optimal constants and remainder terms
Vitaly Moroz, Jean Van Schaftingen
Using a groundstate transformation, we give a new proof of the optimal Stein-Weiss inequality of Herbst [\int_{\R^N} \int_{\R^N} \frac{φ(x)}{\abs{x}^\fracα{2}} I_α(x - y) \frac{φ(y…