Lukas Koch

collaborators

Showing math.APShow all

4 papers · 1 filter

math.AP2020

Energy minimisers with prescribed Jacobian

André Guerra, Lukas Koch, Sauli Lindberg

We study the symmetry and uniqueness of maps which minimise the $n p$ -Dirichlet energy, under the constraint that their Jacobian is a given radially symmetric function $f$ . We find…

math.AP2020

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 $T$ satisfying certain structural assumptions, our main theorem states that the following claims are equivalent: i) $T$ is surjective, ii) $T$ is open at z…

math.AP2020

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, $det D u = f$ , where $f$ is integrable and bounded away from zero. In…

math.AP2020

Boundary regularity for manifold constrained $p (x)$ -harmonic maps

Iwona Chlebicka, Cristiana De Filippis, Lukas Koch

We prove partial and full boundary regularity for manifold constrained $p (x)$ -harmonic maps.

Energy minimisers with prescribed Jacobian

Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs

The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces

Boundary regularity for manifold constrained p(x)-harmonic maps

Boundary regularity for manifold constrained $p (x)$ -harmonic maps