Publications
PeerReviewed Publications:
 Unique Continuation for Fractional Schrödinger Equations with Rough Potential, ArXiv Preprint, Communications in Partial Differential Equations, 40.1 (2015): 77114,
 On the Backward Uniqueness Property of the Heat Equation in TwoDimensional Conical Domains, ArXiv Preprint, manuscripta mathematica, July 2015, Volume 147, Issue 3, pp 415436,
 The CubictoOrthorhombic Phase Transition  Rigidity and NonRigidity Properties in the Linear Theory of Elasticity, MPI MIS Preprint, Archive for Rational Mechanics and Analysis, July 2016, Volume 221, Issue 1, pp 23106,
 A Rigidity Result for a Reduced Model of a CubictoOrthorhombic Phase Transition in the Geometrically Linear Theory of Elasticity, ArXiv Preprint, Journal of Elasticity, April 2016, Volume 123, Issue 2, pp 137177,
 (with Georgy Kitavtsev and Stephan Luckhaus) Surface Energies Arising in Microscopic Modeling of Martensitic Transformations, ArXiv Preprint, Mathematical Models and Methods in Applied Sciences, 25.04 (2015): 647683,
 On quantitative unique continuation properties of fractional Schrödinger equations: Doubling, vanishing order and nodal domain estimates, Trans. Amer. Math. Soc. 369 (2017), 23112362,
 (with Herbert Koch and Wenhui Shi) The variable coefficient thin obstacle problem: Carleman estimates, ArXiv Preprint, Advances in Mathematics, Oct. 2016, Vol. 301, pp. 820–866,
 (with Herbert Koch and Wenhui Shi) The variable coefficient thin obstacle problem: Optimal regularity and regularity of the regular free boundary, ArXiv Preprint, Annales de l'Institut Henri Poincaré / C, 34 (2017) 4, p. 845897,
 (with Georgy Kitavtsev and Stephan Luckhaus) Surface Energies Emerging in a Microscopic, TwoDimensional TwoWell Problem, ArXiv Preprint, Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 147 (2017) 5, p.10411089,
 (with Herbert Koch and Wenhui Shi) The Variable Coefficient Thin Obstacle Problem: Higher Regularity, ArXiv Preprint, Advances in Differential Equations Volume 22, Numbers 1112, November/December 2017,
 (with Herbert Koch and Wenhui Shi) Higher Regularity for the fractional thin obstacle problem, ArXiv Preprint, New York journal of mathematics, 25 (2019), p. 745838,
 (with Christian Zillinger and Barbara Zwicknagl) Higher Sobolev regularity of convex integration solutions in elasticity : the planar geometrically linearized hexagonaltorhombic phase transformation, ArXiv Preprint, Journal of elasticity, 138 (2020) 1, p. 176,
 (with Wenhui Shi) Optimal Regularity for the Thin Obstacle Problem with C^{0,α} Coefficients, ArXiv Preprint, Calc. Var. (2017) 56: 129,
 Quantitative Invertibility and Approximation for the Truncated Hilbert and Riesz Transforms ArXiv Preprint, Revista Matemática Iberoamericana, 35 (2019) 7, p. 19972024,
 (with Mikko Salo) The fractional Calderón problem: low regularity and stability, ArXiv Preprint, Nonlinear analysis / A, 193 (2020), 111529,
 (with Mikko Salo) Quantitative Approximation Properties for the Fractional Heat Equation, ArXiv Preprint, Mathematical control and related fields, 10 (2020) 1, p. 126,
 (with Mikko Salo) Quantitative Runge Approximation and Inverse Problems, ArXiv Preprint, International mathematics research notices, 2019 (2019) 20, p. 62166234.
 (with Christian Zillinger and Barbara Zwicknagl) Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(Klc), ArXiv Preprint, SIAM journal on mathematical analysis, 50 (2018) 4, p. 37913841.
 (with Jamie M Taylor and Christian Zillinger) Convex integration arising in the modelling of shapememory alloys: some remarks on rigidity, flexibility and some numerical implementations ArXiv Preprint, Journal of nonlinear science, 29 (2019) 5, p. 21372184.
 (with Tuhin Ghosh, Mikko Salo and Gunther Uhlmann) Uniqueness and reconstruction for the fractional Calderón problem with a single measurement, ArXiv Preprint, to appear in Journal of functional analysis.
 (with Mikko Salo) Exponential instability in the fractional Calderón problem, ArXiv Preprint, Inverse problems, 34 (2018) 4, 045003.
 Unique continuation for sublinear elliptic equations based on Carleman estimates, ArXiv Preprint, Journal of differential equations, 265 (2018) 11, p. 60096035.
 (with Eva Sincich) Lipschitz stability for the finite dimensional fractional Calderón problem with finite Cauchy data, ArXiv Preprint, Inverse problems and imaging, 13 (2019) 5, p. 10231044.
 (with JennNan Wang) On the fractional Landis conjecture, ArXiv Preprint, Journal of functional analysis, 277 (2019) 9, p. 32363270.
 (with Mihajlo Cekić and YiHsuan Lin) The Calderón problem for the fractional Schrödinger equation with drift, ArXiv Preprint, to appear in Calc. Var. and PDE.
 (with MaríaÁngeles GarcíaFerrero) Strong unique continuation for the higher order fractional Laplacian , ArXiv Preprint, Mathematics in engineering, 1 (2019) 4, p. 715774.
 (with Georgy Kitavtsev, Gianluca Lauteri, Stephan Luckhaus) A compactness and structure result for a discrete multiwell problem with SO(n) symmetry in arbitrary dimension, ArXiv Preprint, Archive for rational mechanics and analysis, 232 (2019) 1, p. 531555.
 (with RuYu Lai, YiHsuan Lin) The Calderón problem for a spacetime fractional parabolic equation, accepted in SIAM Journal on Mathematical Analysis.
 (with Francesco Della Porta) Convex integration solutions for the geometrically nonlinear twowell problem with higher Sobolev regularity, accepted in Mathematical Models and Methods in Applied Sciences.
 (with Pierluigi Cesana, Francesco Della Porta, Christian Zillinger, Barbara Zwicknagl) Exact constructions in the (nonlinear) planar theory of elasticity : from elastic crystals to nematic elastomers, accepted in Archive for rational mechanics and analysis.
 (with Eva Sincich) On Runge approximation and Lipschitz stability for a finitedimensional Schrödinger inverse problem, accepted in Applicable Analysis.
Preprints:

(with Aingeru FernándezBertolin, Luz Roncal, Diana Stan) Discrete Carleman estimates and three balls inequalities, submitted, ArXiv Preprint.

(with MaríaÁngeles GarcíaFerrero) On Two Methods for Quantitative Unique Continuation Results for Some Nonlocal Operators, submitted, ArXiv Preprint.

(with Giovanni Covi) On some partial data Calderón type problems with mixed boundary conditions, ArXiv Preprint.
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Latest Revision:
20200725