41 citations · 158 across the 29 of their papers we have counts for
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Non-uniqueness of Leray solutions of the forced Navier-Stokes equations
Dallas Albritton, Elia Brué, Maria Colombo
In the seminal work [39], Leray demonstrated the existence of global weak solutions to the Navier-Stokes equations in three dimensions. We exhibit two distinct Leray solutions with…
Optimal regularity for the fully nonlinear thin obstacle problem
Maria Colombo, Xavier Fernández-Real, Xavier Ros-Oton
In this work we establish the optimal regularity for solutions to the fully nonlinear thin obstacle problem. In particular, we show the existence of an optimal exponent such…
Instability and nonuniqueness for the Euler equations in vorticity form, after M. Vishik
Dallas Albritton, Elia Brué, Maria Colombo +4
In this expository work, we present Vishik's theorem on non-unique weak solutions to the two-dimensional Euler equations on the whole space, \[ \partial_t ω+ u \cdot \nabla ω= f \,…
Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space
Elia Brué, Maria Colombo
For the two dimensional Euler equations, a classical result by Yudovich states that solutions are unique in the class of bounded vorticity; it is a celebrated open problem whether…
First order expansion in the semiclassical limit of the Levy-Lieb functional
Maria Colombo, Simone Di Marino, Federico Stra
We prove the conjectured first order expansion of the Levy-Lieb functional in the semiclassical limit, arising from Density Functional Theory (DFT). This is accomplished by interpr…
A transmission problem for -Laplacian
Maria Colombo, Sunghan Kim, Henrik Shahgholian
In this paper, we consider a double-phase problem characterised by a transmission that takes place across the zero level "surface" of the minimiser of the functional $$ J(v,Ω) = \i…