Markus Hansen

Position Postdoc e-mail markus.hansenma.tum.de Telephone +49 (0) 89 289 17488 Address Faculty of Mathematics Boltzmannstraße 3 85748 Garching (Munich) Germany

Research interests

• (Besov)Regularity for elliptic and parabolic PDEs
• Parametric and Random PDEs
• Nonlinear/Adaptive wavelet or Finite element approximation
• (Wavelet characterisations of) Function spaces

Publications

Finished work

1. M. Hansen and J. Vybiral, The Franke-Jawerth embedding of spaces with dominating mixed smoothness, Georg. J. Math. 16(4), 2009, 667-682.
2. M. Hansen and T. Strobl, First class constrained systems and twisting of courant algebroids by a closed 4-form, in: Fundamental interactions. A memorial volume for Wolfgang Kummer, World Scientific, Singapore/New Jersey/London, 2010.
3. M. Hansen and W. Sickel, Best m-term approximation and Lizorkin-Triebel spaces, J. Approx. Theory 163(8), 2011, 923-954.
4. M. Hansen and W. Sickel, Best m-term approximation and tensor products of Sobolev and Besov spaces - the case of non-compact embeddings, East J. Approx. 16(4), 2010, 345-388.
5. M. Hansen and W. Sickel, Best m-term approximation and Sobolev-Besov spaces of dominating mixed smoothness - the case of compact embeddings, Constr. Approx. 36(1), 2012, 1-51.
6. M. Hansen, Nonlinear approximation and function spaces of dominating mixed smoothness. Thesis, Jena, 2010.
7. M. Hansen, On tensor products of quasi-Banach spaces, Technical report 2010-31, Seminar for Applied Mathematics, ETH Zürich, 2010.
8. M. Hansen and C. Schwab, Analytic regularity and nonlinear approximation of a class of parametric semilinear PDEs, Math. Nachr. 286(8-9), 832-860.
9. M. Hansen and C. Schwab, Sparse adaptive approximation of high-dimensional parametric initial value problems, Vietnam J. Math. 41(2), 181-215.
10. M. Hansen, C. Schillings, C. Schwab, Sparse adaptive approximation of high-dimensional, parametric initial value ODEs, to appear in: Proceedings of the 5th International conference of high performance computing, Springer, 2013.
11. M. Hansen, n-term approximation rates and Besov regularity for elliptic PDEs on polyhedral domains, to appear in J. Found. Comp. Math., doi: 10.1007/s10208-014-9224-x

In preparation

• M. Hansen, A new regularity result for elliptic PDEs on polyhedral domains and its application of adaptive approximation schemes
• M. Hansen, Higher spatial regularity for parametric PDEs
• M. Hansen, A lower bound for Kolmogorov widths of solutions of parametric families of elliptic PDEs

News

2014
February 3, 2014	Started as PostDoc at M15
March 31 - April 3, 2014	Attended the SIAM conference on Uncertainty Quantification in Savannah, USA.