Angkana Rüland





Max Planck Institute for Mathematics in the Sciences
Inselstraße 22
04103 Leipzig
Germany

Email: rueland"at"mis.mpg.de
Phone: +49 (341) 9959 953


Research interests

  • Fractional Schrödinger equations,
  • Unique Continuation and applications to inverse problems,
  • Obstacle type free boundary value problems,
  • Elasticity with applications to shape-memory alloys.

Teaching

  • Leipzig, Winter 18/19: Seminar Inverse Spectral Theory , SG 3-14, Thursdays 9:15-10:45
  • Leipzig, Summer 18: The Calderón Problem, Augusteum A 314, Thursdays 13:15-14:45
  • Oxford, MT 16: Lecture C5.1 - Solid Mechanics
  • Oxford, MT 15: Two classes B5.2 - Applied Partial Differential Equations
  • Oxford, TT 15: Revision classes: Differential Equations 2, Integral Transforms
  • Oxford, HT 15: College tutorials on Differential Equations 2, Integral Transforms
  • Oxford, MT 14: Two classes in B5.1 - Techniques of Applied Mathematics
  • Bonn, Winter 13/14: Teaching Assistant V1G1 - Analysis I
  • Bonn, Summer 13 (joint with Prof. Dr. Herbert Koch): Seminar S1G1 - Seminar eindimensionale Dynamik

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 PreprintAdvances 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, (accepted in Annales de l'Institut Henri Poincaré),
    • (with Georgy Kitavtsev and Stephan Luckhaus) Surface Energies Emerging in a Microscopic, Two-Dimensional Two-Well Problem, ArXiv Preprint (accepted Proceedings of the Royal Society of Edinburgh, Section: A Mathematics),
    • (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 (submitted),
    • (with Christian Zillinger and Barbara Zwicknagl) Higher Sobolev Regularity of Convex Integration Solutions in Elasticity, ArXiv Preprint (submitted),
    • (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 (submitted),
    • (with Mikko Salo) The fractional Calderón problem: low regularity and stability, ArXiv Preprint (submitted),
    • (with Mikko Salo) Quantitative Approximation Properties for the Fractional Heat Equation, ArXiv Preprint (submitted),
    • (with Mikko Salo) Quantitative Runge Approximation and Inverse Problems, ArXiv Preprint (submitted).
    • (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 (submitted).
    • (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 (submitted).
    • (with Tuhin Ghosh, Mikko Salo and Gunther Uhlmann) Uniqueness and reconstruction for the fractional Calderón problem with a single measurement, ArXiv Preprint (submitted).
    • Unique continuation for sublinear elliptic equations based on Carleman estimates, ArXiv Preprint (submitted).

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