Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Barbara Zwicknagl - Publikationen

Preprints 


(with L. Abel and J. Ginster) A scaling law for a model of epitaxially strained elastic films with dislocations, submitted (2024) [arXiv]

 


Peer-reviewed publications

    1. (with J. Ginster, G. Hayrapetyan, and A. Pesic) A sharp interface limit of a nonlocal variational model for pattern formation in biomembranes, accepted for publication in SIAM Journal on Mathematical Analysis [CVGMT preprint]

    2. (with J. Ginster) Energy scaling laws for microstructures: from helimagnets to martensites, Calculus of Variations and Partial Differential Equations  63:8 (2024), link

    3. (with S. Conti, M. Lenz, M. Rumpf, and J. Verhülsdonk) Microstructure of macrointerfaces in shape-memory alloys, Journal of the Mechanics and Physics of Solids 179, 105343 (2023), link

    4. (with S. Conti, M. Lenz, M. Rumpf, and J. Verhülsdonk) Geometry of needle-like microstructures in shape-memory alloys, Shape Memory and Supererlasticity, invited submission selected from presentations at ESOMAT 2022,  link (2023)

    5. (with S. Conti) The tapering length of needles in martensite/martensite macrotwins, Archive for Rational Mechanics and Analysis 247:63 (2023) [CVGMT preprint]
       
    6. (with J. Ginster) Energy Scaling Law for a Singularly Perturbed Four-Gradient Problem in Helimagnetism, Journal of Nonlinear Sciences 33, 20 (2023), link (open access)

    7. (with S. Conti, J. Diermeier, and M. Koser) Asymptotic Self-Similarity of Minimizers and Local Bounds in a Model of Shape-Memory Alloys, Journal of Elasticity 147, pp. 149-200 (2021), link (open access)

       

    8. (with S. Conti, M. Lenz, N. Lüthen, and M. Rumpf) Geometry of martensite needles in shape memory alloys, Comptes Rendus Math. 9-10, pp. 1047-1057 (2020) [arXiv]

    9. (with S. Conti, J. Diermeier, and D. Melching) Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys, ESAIM:COCV 26, 115 (2020) [arXiv]

    10. (with P. Cesana, F. Della Porta, A. Rüland and C. Zillinger) Exact Constructions in the (Non-Linear) Planar Theory of Elasticity: From Elastic Crystals to Nematic Elastomers,  Archive for Rational Mechanics and Analysis 237(1), pp. 383-445 (2020) [arXiv]
       
    11. (with A. Rüland and C. Zillinger) Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Planar Geometrically Linearized Hexagonal-to-Rhombic Phase Transformation, Journal of Elasticity 138, pp. 1-76 (2020) (open access)
       
    12. (with A. Rüland and C. Zillinger) Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int($K^{lc}$), SIAM J. Math. Anal. 50(4), pp. 3791-3841 (2018) [arXiv]
       
    13. (with S. Conti and M. Klar) Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity, Proceedings of the Royal Society A 473(2203), (2017)

    14. (with M. Griebel and C. Rieger) Regularized kernel based reconstruction in generalized Besov spaces, Foundations of Computational Mathematics 18(2), pp. 459-508 (2018), DOI: 10.1007/s10208-017-9346-z, [INS preprint]

    15. (with S. Conti and J. Diermeier) Deformation concentration for martensitic microstructures in the limit of low volume fraction, Calculus of Variations and Partial Differential Equations 56:16 (2017), [arXiv]

    16. (with I. Fonseca, G. Hayrapetyan and G. Leoni) Domain formation in membranes near the onset of instability, Journal of Nonlinear Science 26 (5), pp. 1191-1225 (2016), [CNA preprint]

    17. (with S. Conti) Low volume-fraction microstructures in martensites and crystal plasticity, Mathematical Models and Methods in Applied Sciences 26, pp.1319-1355 (2016) [arXiv]

    18. (with P. Bella and M. Goldman) Study of island formation in epitaxially strained films on unbounded domains, Archive for Rational Mechanics and Analysis 218(1), pp. 163-217 (2015), [article], [arXiv]

    19. (with M. Griebel and C. Rieger) Multiscale approximation and reproducing kernel Hilbert space methods, SIAM Journal on Numerical Analysis 53(2), pp. 852-873 (2015), [article], [INS preprint]

    20. (with I. Fonseca and A. Pratelli) Shapes of epitaxially grown quantum dots, Archive for Rational Mechanics and Analysis 214(2), pp. 359-401 (2014), [article], [CNA preprint]

    21. (with M. Goldman) Scaling law and reduced models for epitaxially strained crystalline films, SIAM Journal on Mathematical Analysis 46, pp. 1-24 (2014), [article], [CNA preprint]

    22. (with C. Rieger) Improved Exponential Convergence Rates by Oversampling Near the Boundary, Constructive Approximation 39(2), pp. 323-341 (2014), [article]

    23. (with R. Choksi and I. Fonseca) A few remarks on variational models for denoising, Communications in Mathematical Sciences 12(5), pp. 843-857 (2014),  [article], [CNA preprint]

    24. Microstructures in low-hysteresis shape memory alloys: scaling regimes and optimal needle shapes, Archive for Rational Mechanics and Analysis 213(2), pp. 355-421 (2014), [article], [CNA preprint]

    25. (with R. Schaback) Interpolation and Approximation in Taylor Spaces, Journal of Approximation Theory 171, pp. 65-83 (2013), [article], [preprint]

    26. (with C. Rieger) Sampling Inequalities for Infinitely Smooth Functions, with Applications to Interpolation and Machine Learning, Advances in Computational Mathematics 32 pp. 103-129 (2010), [article], [MPI MiS preprint]

    27. (with C. Rieger and R. Schaback) Sampling and Stability, in M. Dahlen et al. (Eds.): Mathematical Methods for Curves and Surfaces 2008, Lecture Notes in Computer Science 5862, pp. 347–369 (2010), [article]

    28. (with C. Rieger) Deterministic Error Analysis of Support Vector Regression and Related Regularized Kernel Methods, Journal of Machine Learning Research 10, pp. 2115-2132 (2009), [article] (open access)

    29. Power series kernels, Constructive Approximation 29, pp. 61-84 (2009), [article] (open access)