- with E. Gallagher: The ∞-elastica problem on a Riemannian manifold, preprint, 2022. arXiv:2202.07407 [math.DG].
- Regularity of gradient vector fields giving rise to finite Caccioppoli partitions, Calculus of Variations and Partial Differential Equations
**61**(2022), 183. - The streamlines of ∞-harmonic functions obey the inverse mean curvature flow, Communications in Partial Differential Equations (Latest Articles), 2022.
- with J. Roberts: Partial regularity for harmonic maps into spheres at a singular or degenerate free boundary, Journal of Geometric Analysis
**32**(2022), 58. - with R. Ignat: Separation of domain walls with nonlocal interaction and their renormalised energy by Γ-convergence in thin ferromagnetic films, Journal of Differential Equations
**339**(2022), 395–475. - Structure and classification results for the ∞-elastica problem, to appear in the American Journal of Mathematics; arXiv:1908.01569 [math.DG].
- with R. Ignat: Energy minimisers of prescribed winding number in an S
^{1}-valued nonlocal Allen-Cahn type model, Advances in Mathematics**357**(2019), 106819. - with N. Katzourakis: Existence, uniqueness and structure of second order absolute minimisers, Archive for Rational Mechanics and Analysis
**231**(2019), 1615–1634. - Structure and rigidity of functions in BV2

loc(ℝ^{2}) with gradients taking only 3 values, Proceedings of the London Mathematical Society**116**(2018), 813–846. - with R. Ignat: Néel walls with prescribed winding number and how a nonlocal term can change the energy landscape, Journal of Differential Equations
**263**(2017), 5846–5901. - with P. Hornung: Existence of equivariant biharmonic maps, International Mathematics Research Notices
**2016**, 2397–2422. - with R. Ignat: Interaction energy of domain walls in a nonlocal Ginzburg-Landau type model from micromagnetics, Archive for Rational Mechanics and Analysis
**221**(2016), 419–485. - An
*L*regularity theory for harmonic maps, Transactions of the American Mathematical Society^{p}**367**(2015), 1–30. - Geroch monotonicity and the construction of weak solutions of the inverse mean curvature flow, Asian Journal of Mathematics
**19**(2015), 357–376. - Singular perturbation problems involving curvature,
*Differential Geometry and Continuum Mechanics*, 49–75, Springer Proceedings in Mathematics & Statistics, 137, Springer, Cham, 2015. - with P. Hornung: Intrinsically
*p*-biharmonic maps Calculus of Variations and Partial Differential Equations**51**(2014), 597–620. - with P. Hornung: A reformulation of the biharmonic map equation, Journal of Geometric Analysis
**24**(2014), 1201–1210. - with M. Kurzke, C. Melcher, and D. Spirn: Vortex dynamics in the presence of excess energy for the Landau-Lifshitz-Gilbert equation, Calculus of Variations and Partial Differential Equations
**49**(2014), 1019–1043. - A construction of biharmonic maps into homogeneous spaces, Communications in Analysis & Geometry
**22**(2014), 451–468. - A geometric Ginzburg-Landau problem, Mathematische Zeitschrift
**273**(2013), 771–792. Erratum in: Mathematische Zeitschrift**276**(2014), 611–612. - with M. Kurzke and C. Melcher: Vortex motion for the Landau-Lifshitz-Gilbert equation with applied magnetic field,
*Singular Phenomena and Scaling in Mathematical Models*, 113–131, Springer, Heidelberg, 2013. - Towards a variational theory of phase transitions involving curvature, Proceedings of the Royal Society of Edinburgh Section A – Mathematics
**142**(2012), 839–865. - with R. Ignat: A zigzag pattern in micromagnetics, Journal de Mathématiques Pures et Appliquées
**98**(2012), 138–159. - with P. Hornung: Energy identity for intrinsically biharmonic maps in four dimensions, Analysis & PDE
**5**(2012), 61–80. - with P. Hornung: Intrinsically biharmonic maps into homogeneous spaces Advances in Calculus of Variations
**5**(2012), 411–425. - with H. Schwetlick: Minimizers of a weighted maximum of the Gauss curvature, Annals of Global Analysis and Geometry
**41**(2012), 199–207. - with M. Kurzke, C. Melcher, and D. Spirn: Ginzburg–Landau vortices driven by the Landau–Lifshitz–Gilbert equation, Archive for Rational Mechanics and Analysis
**199**(2011), 843–888. - Intrinsic semiharmonic maps, Journal of Geometric Analysis
**21**(2011), 588–598. - with M. Kurzke and C. Melcher: Vortex motion for the Landau-Lifshitz-Gilbert equation with spin transfer torque SIAM Journal on Mathematical Analysis (SIMA)
**43**(2011), 1099–1121. - Regularity of minimizing extrinsic polyharmonic maps in the critical dimension, Manuscripta Mathematica
**131**(2010), 475–485. - A Trudinger type inequality for maps into a Riemannian manifold Annals of Global Analysis and Geometry
**35**(2009), 83–90. - Weak solutions of a biharmonic map heat flow, Advances in Calculus of Variations
**2**(2009), 73–92. - with M. Kurzke, C. Melcher, and D. Spirn: Dynamics for Ginzburg-Landau vortices under a mixed flow, Indiana University Mathematics Journal
**58**(2009), 2597–2621. - Ginzburg-Landau Vortex Lines and the Elastica Functional, Communications in Contemporary Mathematics
**11**(2009), 71–107. - On the energy of domain walls in ferromagnetism, Interfaces and Free Boundaries
**11**(2009) 399–419. - A second-order variational problem with a lack of coercivity, Proceedings of the London Mathematical Society
**96**(2008), 199–226. - A variational problem pertaining to biharmonic maps Communications in Partial Differential Equations
**33**(2008), 1654–1689. - Analysis and Stochastics of Growth Processes and Interface Models, edited by P. Mörters, R. Moser, M. Penrose, H. Schwetlick, and J. Zimmer, Oxford University Press, Oxford, 2008.
- Energy concentration for the Landau–Lifshitz equation, Annales de l'Institut Henri Poincaré (C) Non Linear Analysis,
**25**(2008), 987–1013. - The inverse mean curvature flow as an obstacle problem, Indiana University Mathematics Journal
**57**(2008), 2235–2256. - On a variational problem with non-differentiable constraints, Calculus of Variations and Partial Differential Equations,
**29**(2007), 119–140. - The inverse mean curvature flow and
*p*-harmonic functions, Journal of the European Mathematical Society**9**(2007), 77–83. - with M. Kurzke, and C. Melcher: Domain walls and vortices in thin ferromagnetic films,
*Analysis, modeling and simulation of multiscale problems*, 249–298, Springer, Berlin, 2006. - Remarks on the regularity of biharmonic maps in four dimensions, Communications on Pure and Applied Mathematics
**59**(2006), 317–329. - A higher order asymptotic problem related to phase transitions, SIAM Journal on Mathematical Analysis (SIMA)
**37**(2005), 712–736. - Energy concentration for almost harmonic maps and the Willmore functional, Mathematische Zeitschrift
**251**(2005), 293–311. - Moving boundary vortices for a thin-film limit in micromagnetics, Communications on Pure and Applied Mathematics
**58**(2005), 701–721. - Partial regularity for harmonic maps and related problems, World Scientific, 2005.
- The blowup behavior of the biharmonic map heat flow in four dimensions, International Mathematics Research Papers (IMRP)
**2005**, 351–402. - Boundary vortices for thin ferromagnetic films, Archive for Rational Mechanics and Analysis
**174**(2004), 267–300. - An ε-regularity result for generalized harmonic maps into spheres, Electronic Journal of Differential Equations
**2003**1–7. - Energy concentration for thin films in micromagnetics, Mathematical Models & Methods in Applied Sciences
**13**(2003), 767–784 - Ginzburg-Landau vortices for thin ferromagnetic films, Applied Mathematics Research Express (AMRE)
**2003**, 1–32. - Regularity for the approximated harmonic map equation and application to the heat flow for harmonic maps, Mathematische Zeitschrift
**243**(2003), 263–289. - Stationary measures and rectifiability, Calculus of Variations and Partial Differential Equations
**17**(2003), 357–368. - Unique solvability of the Dirichlet problem for weakly harmonic maps, Manuscripta Mathematica
**105**(2001), 379–399.