Publications

Peer-Reviewed Publications:

Unique Continuation for Fractional Schrödinger Equations with Rough Potential, ArXiv Preprint, Communications in Partial Differential Equations, 40.1 (2015): 77-114,
On the Backward Uniqueness Property of the Heat Equation in Two-Dimensional Conical Domains, ArXiv Preprint, manuscripta mathematica, July 2015, Volume 147, Issue 3, pp 415-436,
The Cubic-to-Orthorhombic Phase Transition - Rigidity and Non-Rigidity Properties in the Linear Theory of Elasticity, MPI MIS Preprint, Archive for Rational Mechanics and Analysis, July 2016, Volume 221, Issue 1, pp 23-106,
A Rigidity Result for a Reduced Model of a Cubic-to-Orthorhombic Phase Transition in the Geometrically Linear Theory of Elasticity, ArXiv Preprint, Journal of Elasticity, April 2016, Volume 123, Issue 2, pp 137-177,
(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): 647-683,
On quantitative unique continuation properties of fractional Schrödinger equations: Doubling, vanishing order and nodal domain estimates, Trans. Amer. Math. Soc. 369 (2017), 2311-2362,
(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. 845-897,
(with Georgy Kitavtsev and Stephan Luckhaus) Surface Energies Emerging in a Microscopic, Two-Dimensional Two-Well Problem, ArXiv Preprint, Proceedings of the Royal Society of Edinburgh, Section: A Mathematics, 147 (2017) 5, p.1041-1089,
(with Herbert Koch and Wenhui Shi) The Variable Coefficient Thin Obstacle Problem: Higher Regularity, ArXiv Preprint, Advances in Differential Equations Volume 22, Numbers 11-12, 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. 745-838,
(with Christian Zillinger and Barbara Zwicknagl) Higher Sobolev regularity of convex integration solutions in elasticity : the planar geometrically linearized hexagonal-to-rhombic phase transformation, ArXiv Preprint, Journal of elasticity, 138 (2020) 1, p. 1-76,
(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. 1997-2024,
(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. 1-26,
(with Mikko Salo) Quantitative Runge Approximation and Inverse Problems, ArXiv Preprint, International mathematics research notices, 2019 (2019) 20, p. 6216-6234.
(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. 3791-3841.
(with Jamie M Taylor and Christian Zillinger) Convex integration arising in the modelling of shape-memory alloys: some remarks on rigidity, flexibility and some numerical implementations ArXiv Preprint, Journal of nonlinear science, 29 (2019) 5, p. 2137-2184.
(with Tuhin Ghosh, Mikko Salo and Gunther Uhlmann) Uniqueness and reconstruction for the fractional Calderón problem with a single measurement, ArXiv Preprint, Journal of Functional Analysis 279.1 (2020): 108505.
(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. 6009-6035.
(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. 1023-1044.
(with Jenn-Nan Wang) On the fractional Landis conjecture, ArXiv Preprint, Journal of functional analysis, 277 (2019) 9, p. 3236-3270.
(with Mihajlo Cekić and Yi-Hsuan Lin) The Calderón problem for the fractional Schrödinger equation with drift, ArXiv Preprint, Calculus of Variations and Partial Differential Equations 59.3 (2020): 1-46.
(with María-Ángeles García-Ferrero) Strong unique continuation for the higher order fractional Laplacian , ArXiv Preprint, Mathematics in engineering, 1 (2019) 4, p. 715-774.
(with Georgy Kitavtsev, Gianluca Lauteri, Stephan Luckhaus) A compactness and structure result for a discrete multi-well problem with SO(n) symmetry in arbitrary dimension, ArXiv Preprint, Archive for rational mechanics and analysis, 232 (2019) 1, p. 531-555.
(with Ru-Yu Lai, Yi-Hsuan Lin) The Calderón problem for a space-time fractional parabolic equation, SIAM Journal on Mathematical Analysis 52.3 (2020): 2655-2688.
(with Francesco Della Porta) Convex integration solutions for the geometrically non-linear two-well problem with higher Sobolev regularity, Mathematical Models and Methods in Applied Sciences, 30(03), 611-651.
(with Pierluigi Cesana, Francesco Della Porta, Christian Zillinger, Barbara Zwicknagl) Exact constructions in the (non-linear) planar theory of elasticity : from elastic crystals to nematic elastomers, Archive for Rational Mechanics and Analysis 237.1 (2020): 383-445.
(with Eva Sincich) On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem, Applicable Analysis (2020): 1-12.
(with María-Ángeles García-Ferrero) On Two Methods for Quantitative Unique Continuation Results for Some Nonlocal Operators, submitted, ArXiv Preprint, Communications in Partial Differential Equations 45.11 (2020): 1512-1560.
(with Giovanni Covi) On some partial data Calderón type problems with mixed boundary conditions, ArXiv Preprint, accepted for publication in Journal of Differential Equations.
(with Aingeru Fernández-Bertolin, Luz Roncal, Diana Stan) Discrete Carleman estimates and three balls inequalities, submitted, ArXiv Preprint, accepted for publication in Calc. Var. PDE.
On Single Measurement Stability for the Fractional Calderón Problem, ArXiv Preprint, SIAM J. Math. Anal., 53(5), 5094–5113.
(with Francesco Della Porta, Jamie M Taylor, Christian Zillinger) On a probabilistic model for martensitic avalanches incorporating mechanical compatibility, ArXiv Preprint, Nonlinearity, Volume 34, Number 7, 4844.
(with María-Ángeles García-Ferrero and Wiktoria Zatoń): Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation, ArXiv Preprint, accepted in Inverse Problems & Imaging.
(with Herbert Koch and Mikko Salo): On Instability Mechanisms in Inverse Problems, ArXiv Preprint, Ars Inveniendi Analytica (2021), Paper No. 7, 93 pp.
(with Wenhui Shi): Higher Regularity for the Signorini Problem for the Homogeneous, Isotropic Lamé System, ArXiv Preprint, Nonlinear Analysis 217 (2022): 112762.
(with Antonio Tribuzio): On the Energy Scaling Behaviour of a Singularly Perturbed Tartar Square, ArXiv Preprint, Archive for Rational Mechanics and Analysis, 243(1), 401-431.
(with G. Covi and María Ángeles García-Ferrero): On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols, ArXiv Preprint, Journal of Differential Equations, Volume 341, 2022, 79-149.

Preprints:

(with Antonio Tribuzio): On the Energy Scaling Behaviour of Singular Perturbation Models Involving Higher Order Laminates, ArXiv Preprint.
(with with Aingeru Fernández-Bertolin, Luz Roncal) On (Global) Unique Continuation Properties of the Fractional Discrete Laplacian, ArXiv Preprint.
(with Antonio Tribuzio): On Scaling Laws for Multi-Well Nucleation Problems without Gauge Invariances, ArXiv Preprint.
(with Ibrokhimbek Akramov, Hans Knüpfer and Martin Kružík): Minimal Energy for Geometrically Nonlinear Elastic Inclusions in Two Dimensions, ArXiv Preprint.
(with Camillo Tissot): On Scaling Properties for Two-State Problems and for a Singularly Perturbed T3 Structure, ArXiv Preprint.
(with Theresa M. Simon): On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation, ArXiv Preprint.

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Latest Revision: 2022-10-12