RESEARCH

My research can be broadly split into three different themes.

Regularity in the vectorial Calculus of Variations:

• A note on improved differentiability for the Banach-space valued Finsler g-Laplacian
  With M. Goering Comptes Rendus. Mathématique, 361 (2023).
• Boundary regularity results for minimisers of convex functionals with (p,q)-growth
  With C. Irving. Advances in Nonlinear Analysis, 12, no.1 (2023).
• Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth
  Calculus of Variations and Partial Differential Equations, 61 (2022).
• Global higher integrability for minimisers of convex functionals with (p,q)-growth
  Calculus of Variations and Partial Differential Equations, 60, no. 63 (2021).
• Boundary regularity for manifold constrained p(x)-harmonic maps.
  With I. Chlebicka and C. de Filippis. Journal of the London Mathematical Society, 60, no. 5(2021).
• On the Lavrentiev gap for convex, vectorial integral functionals
  With M. Ruf and M. Schäffner. Submitted. (2023)
• On global absence of Lavrentiev gap for functionals with (p,q)-growth.
  
• On the validity of the Euler-Lagrange system without growth assumptions.
  With J. Kristensen (2022)
• Quantified Legendreness and the regularity of minima.
  With J. Kristensen and C. de Filippis. Submitted. (2023)

Optimal transportation:

• Geometric linearisation for optimal transport with strongly p-convex cost
  Calculus of Variations and Partial Differential Equations, 63, no. 87(2024).
• Lecture notes on the harmonic approximation to quadratic optimal transport
  With F. Otto (2023)

The Jacobian equation and other nonlinear PDEs:

• Nonlinear open mapping principles, with applications to the Jacobian eq. and other scale-invariant PDEs.
  With A. Guerra and S. Lindberg, (2020). Advances in Mathematics, 415, 108869. (2023)
• The Dirichlet problem for the Jacobian equation in critical and supercritical Sobolev spaces.
  With A. Guerra and S. Lindberg. Calculus of Variations and Partial Differential Equations, 60, no. 55 (2021).
• Energy minimisers with prescribed Jacobian.
  With A. Guerra and S. Lindberg Archive for Rational Mechanics, 242 (2021).

Other areas:

Regularity for quasilinear vectorial elliptic systems through an iterative scheme with numerical applications
Nonlinear Differential Equations and Applications 29(75) (2022).