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Publications and Preprints
On regularity and rigidity of 2×2 differential inclusions into non-elliptic curves. With Xavier Lamy and Guanying Peng.
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Quantitative rigidity of differential inclusions in two dimensions. With Xavier Lamy and Guanying Peng (To appear in International Mathematics Research Notices).
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On optimal regularity estimates for finite-entropy solutions of scalar conservation laws. With Xavier Lamy and Guanying Peng. (To appear in Comptes Rendus Mathematique)
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On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds. With Xavier Lamy and Guanying Peng. (Communications in Partial Differential Equations. Sep 2022)
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Factorization of entropy production of the Eikonal equation and regularity. With Guanying Peng. (To appear in Indiana University Mathematics Journal)
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Rigidity of a non-elliptic differential inclusion related to the Aviles-Giga conjecture. With Xavier Lamy and Guanying Peng. (Arkiv of Rational Mechanics and Analysis. 238 (2020). no.1 383-413.
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On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity. With Guanying Peng. To appear in Calc Var and Partial Differential Equations.
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Null Lagrangian Measures in planes, compensated compactness and conservation laws. With Guanying Peng. (Arkiv of Rational Mechanics and Analysis. Nov 2019. Vol 234. Issue 2. 857-910)
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Regularity of the Eikonal equation with two vanishing entropies. With Guanying Peng. (Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 2, 481–516.)
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Rigidity of pairs of quasiregular mappings whose symmetric part of gradient are close. (Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 1, 23–65)
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On indecomposable sets and applications preprint. ( ESAIM Control Optim. Calc. Var. 20 (2014), no. 2, 612–631)
A generalized Stoilow decomposition for pairs of mappings of integrable dilatation. (Adv. Calc. Var. 7 (2014), no. 3, 327–351).
Differential inclusions, non-absolutely convergent integrals and the first theorem of complex analysis. ( Q. J. Math. 65 (2014), no. 4, 1363–1373)
On functions whose symmetric part of gradient agree and a generalization of Reshetnyak's compactness theorem. ( Calc. Var. Partial Differential Equations 48 (2013), no. 3-4, 625–665).
Regularity of sets with quasiminimal boundary surfaces in metric spaces. With Juha Kinnunen, Riikka Korte, Nageswari Shanmugalingam. ( J. Geom. Anal. 23 (2013), no. 4, 1607–1640)
A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity. ( ESAIM Control Optim. Calc. Var. 18 (2012), no. 2, 383–400).
A quantitative characterisation of functions with low Aviles Giga energy on convex domains. (Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13 (2014), no. 1, 1–66.
On multiwell Liouville Theorems in higher dimension. With J.L. Jerrard. (Adv. Calc. Var. 6 (2013), no. 3, 247–298)
The regularisation of the N-well problem by finite elements and by singular perturbation are scaling equivalent in two dimensions. (ESAIM Control Optim. Calc. Var. 15 (2009))
An L^p two well Liouville Theorem. (Ann. Acad. Sci. Fenn. Math. 33 (2008), no. 2, 439–473)
A Marstrand Theorem for measures with polytope density.
(Math. Ann. 338 (2007), no. 2, 451–474)
A two well Liouville theorem. ESAIM Control Optim. Calc. Var. 11 (2005), no. 3, 310–356.
The two well problem with surface energy. ( Proc. Roy. Soc. Edinburgh Sect. A 136 (2006), no. 4, 795–805)
A Marstrand type theorem for measures with cube density in general dimension. (Math. Proc. Cambridge Philos. Soc. 137 (2004), no. 3, 657–696)
Generalised Touching Point Arguments in Geometric Measure Theory. (Ann. Acad. Sci. Fenn. Math. 28 (2003), no. 2, 415–431)
An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure. (M2AN Math. Model. Numer. Anal. 35 (2001), no. 5, 921–934 M2AN)
Rectifiability of Measures with Locally Uniform Cube Density. (Proc. London Math. Soc. (3) 86 (2003), no. 1, 153–249)