3 citations · 3 across the 2 of their papers we have counts for
6 papers · 1 filter
Oscillations in wave map systems and homogenization of the Einstein equations in symmetry
André Guerra, Rita Teixeira da Costa
In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein--massless…
Energy minimisers with prescribed Jacobian
André Guerra, Lukas Koch, Sauli Lindberg
We study the symmetry and uniqueness of maps which minimise the -Dirichlet energy, under the constraint that their Jacobian is a given radially symmetric function . We find…
Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs
André Guerra, Lukas Koch, Sauli Lindberg
For a nonlinear operator satisfying certain structural assumptions, our main theorem states that the following claims are equivalent: i) is surjective, ii) is open at z…
The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces
André Guerra, Lukas Koch, Sauli Lindberg
We study existence and regularity of solutions to the Dirichlet problem for the prescribed Jacobian equation, , where is integrable and bounded away from zero. In…
Remarks on Ornstein's non-inequality in
Daniel Faraco, André Guerra
We give a very concise proof of Ornstein's non-inequality for first- and second-order operators in two dimensions. The proof just needs a two-dimensional laminate supported o…
Extremal rank-one convex integrands and a conjecture of Šverák
André Guerra
We show that in order to decide whether a given probability measure is laminate it is enough to verify Jensen's inequality in the class of extremal non-negative rank-one convex int…