22 citations · 77 across the 17 of their papers we have counts for
7 papers · 1 filter
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…
Compensated compactness: continuity in optimal weak topologies
André Guerra, Bogdan Raiţă, Matthew R. I. Schrecker
For -homogeneous linear differential operators of constant rank, we study the implication in and $\mathcal{A} v_j\rightarrow \mathcal{A}…
On the necessity of the constant rank condition for estimates
André Guerra, Bogdan Raiţă
We consider a generalization of the elliptic -estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura App…
Numerical evidence towards a positive answer to Morrey's problem
André Guerra, Rita Teixeira da Costa
We report on numerical experiments suggesting that rank-one convexity imples quasiconvexity in the planar case. We give a simple heuristic explanation of our findings.