Publications

Preprints 

1. (with A. Rüland and C. Zillinger) Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Planar Geometrically Linearized Hexagonal-to-Rhombic Phase Transformation, submitted 2018, [arXiv]

Peer-reviewed journal publications 

1. (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 Journal on Mathematical Analysis 50(4), pp. 3791-3841 (2018), [arXiv]
   
   
2. (with M. Griebel and C. Rieger) Regularized kernel based reconstruction in generalized Besov spaces, Foundations of Computational Mathematics 18, pp. 459-508 (2018), [INS preprint]
   
   
3. (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)


4. (with S. Conti and J. Diermeier) Deformation concentration for martensitic microstructures in the limit of low volume fraction, Calculus of Variations and Partial Differential Equations56:16 (2017), [arXiv]


5. (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]


6. (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]


7. (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]


8. (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]


9. (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]


10. (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]


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


12. (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]


13. 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]


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


15. (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]


16. (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)


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

Peer-reviewed conference proceeding 

1. (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]

Other reports 

1. (with P. Bella, I. Fonseca, M. Goldman and A. Pratelli) Epitaxially strained crystalline films: Scaling regimes and beyond, Oberwolfach report No. 54/2013, pp. 3185-3186
2. (with S. Conti and J. Diermeier) Low volume-fraction microstructures in shape memory alloys, Oberwolfach report No. 17/2016, pp. 861-863