13 citations · 33 across the 13 of their papers we have counts for
5 papers · 2 filters
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…
Global higher integrability for minimisers of convex functionals with (p,q)-growth
Lukas Koch
We prove global -regularity for minimisers of convex functionals of the form . regulari…
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…
Boundary regularity for manifold constrained -harmonic maps
Iwona Chlebicka, Cristiana De Filippis, Lukas Koch
We prove partial and full boundary regularity for manifold constrained -harmonic maps.