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Desingularization of vortices for the Euler equation
Didier Smets, Jean Van Schaftingen
We study the existence of stationary classical solutions of the incompressible Euler equation in the plane that approximate singular stationnary solutions of this equation. The con…
Pathological solutions to elliptic problems in divergence form with continuous coefficients
Tianling Jin, Vladimir Maz'ya, Jean Van Schaftingen
We construct a function which is a solution to $\Div (A \nabla u)=0$ in the sense of distributions, where is continuous and $u \not \in…
Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials
Vitaly Moroz, Jean Van Schaftingen
We study the existence of stationnary positive solutions for a class of nonlinear Schroedinger equations with a nonnegative continuous potential V. Amongst other results, we prove…
Explicit approximation of the symmetric rearrangement by polarizations
Jean Van Schaftingen
We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial…
Closure of Smooth Maps in
Augusto C. Ponce, Jean Van Schaftingen
For every , we show that can be strongly approximated by maps in $C^\infty(\Bar{B}^3; S^2)$ if, and only if, the distributional Jacobian of …