Markus Hansen

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
 M. Hansen and J. Vybiral, The FrankeJawerth embedding of spaces with dominating mixed smoothness, Georg. J. Math. 16(4), 2009, 667682.
 M. Hansen and T. Strobl, First class constrained systems and twisting of courant algebroids by a closed 4form, in: Fundamental interactions. A memorial volume for Wolfgang Kummer, World Scientific, Singapore/New Jersey/London, 2010.
 M. Hansen and W. Sickel, Best mterm approximation and LizorkinTriebel spaces, J. Approx. Theory 163(8), 2011, 923954.
 M. Hansen and W. Sickel, Best mterm approximation and tensor products of Sobolev and Besov spaces  the case of noncompact embeddings, East J. Approx. 16(4), 2010, 345388.
 M. Hansen and W. Sickel, Best mterm approximation and SobolevBesov spaces of dominating mixed smoothness  the case of compact embeddings, Constr. Approx. 36(1), 2012, 151.
 M. Hansen, Nonlinear approximation and function spaces of dominating mixed smoothness. Thesis, Jena, 2010.
 M. Hansen, On tensor products of quasiBanach spaces, Technical report 201031, Seminar for Applied Mathematics, ETH Zürich, 2010.
 M. Hansen and C. Schwab, Analytic regularity and nonlinear approximation of a class of parametric semilinear PDEs, Math. Nachr. 286(89), 832860.
 M. Hansen and C. Schwab, Sparse adaptive approximation of highdimensional parametric initial value problems, Vietnam J. Math. 41(2), 181215.
 M. Hansen, C. Schillings, C. Schwab, Sparse adaptive approximation of highdimensional, parametric initial value ODEs, to appear in: Proceedings of the 5th International conference of high performance computing, Springer, 2013.
 M. Hansen, nterm approximation rates and Besov regularity for elliptic PDEs on polyhedral domains, to appear in J. Found. Comp. Math., doi: 10.1007/s102080149224x
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. 