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Least action nodal solutions for the quadratic Choquard equation
Marco Ghimenti, Vitaly Moroz, Jean Van Schaftingen
We prove the existence of a minimal action nodal solution for the quadratic Choquard equation where is…
Applications of Bourgain-Brezis inequalities to Fluid Mechanics and Magnetism
Sagun Chanillo, Jean Van Schaftingen, Po-lam Yung
We apply the borderline Sobolev inequalities of Bourgain-Brezis to the vorticity equation and Navier-Stokes equation in 2D. We take the initial vorticity to be in the space of func…
Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds
Mircea Petrache, Jean Van Schaftingen
Given , a compact Riemannian manifold and a Sobolev map , we construct a map in the Sobolev-Marcinkiewicz…
Approximation of symmetrizations by Markov processes
Justin Dekeyser, Jean Van Schaftingen
Under continuity and recurrence assumptions, we prove that the iteration of successive partial symmetrizations that form a time-homogeneous Markov process, converges to a symmetriz…
Nodal solutions for the Choquard equation
Marco Ghimenti, Jean Van Schaftingen
We consider the general Choquard equations where is a Riesz potential. We construct minimal action odd solutions for $p \in (\fr…
Geometric partial differentiability on manifolds: the tangential derivative and the chain rule
Alexandra Convent, Jean Van Schaftingen
We define the tangential derivative, a notion of directional derivative which is invariant under diffeomorphisms. In particular this derivative is invariant under changes of chart…
Density of bounded maps in Sobolev spaces into complete manifolds
Pierre Bousquet, Augusto C. Ponce, Jean Van Schaftingen
Given a complete noncompact Riemannian manifold , we investigate whether the set of bounded Sobolev maps on the cube is strongly de…