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Lukáš Malý

Title: Visiting Lecturer at University of Gothenburg / Chalmers, Sweden
Current e-mail address: lukas.maly@matfyz.cz
Office: 4428D French Hall
Tel: 513-556-4040
Email: malyls@ucmail.uc.edu

Education

  • PhD, Linköping University, Sweden, 2014 (Mathematics).
  • PhD (double-degree), Charles University in Prague, Czech Republic, 2014 (Mathematical Analysis).
  • Mgr. (≈ MSc), Charles University in Prague, Czech Republic, 2008 (Mathematical Analysis).
  • Bc. (≈ BSc), Charles University in Prague, Czech Republic, 2006 (General Mathematics).

Research Information

Research Support

  • Postdoctoral Scholarship Program in Mathematics, Knut and Alice Wallenberg Foundation. 08-2015 to 07-2017. Status: Active.
  • The Matts Essén Memorial Fund, Swedish Mathematical Society. 06-2013.
  • Research Network “Analysis and Application”, NordForsk. 2011.

Publications

Peer-reviewed Publications

  • Malý, L.: Minimal weak upper gradients in Newtonian spaces based on quasi-Banach function lattices. Ann. Acad. Sci. Fenn. Math., 38 (2013), 727--745. doi:10.5186/aasfm.2013.3831.
  • Malý, L.: Calderón-type theorems for operators with non-standard endpoint behavior on Lorentz spaces. Math. Nachr., 285 (2012), 1450--1465. doi:10.1002/mana.201100095.
  • Malý, L.: Newtonian spaces based on quasi-Banach function lattices. Math. Scand., 119 No. 1 (2016), 133–160.
  • Malý, L.: Regularization of Newtonian functions on metric spaces via weak boundedness of maximal operators. To appear in J. Anal. Math., (2014), arXiv:1404.7068.
  • Malý, L.: Fine properties of Newtonian functions and the Sobolev capacity on metric measure spaces. Rev. Mat. Iberoamericana, 32 (2016), 219–255, doi:10.4171/RMI/884.
  • Malý, L., Shanmugalingam, N., and Snipes, M. (2015). Trace and extension theorems for functions of bounded variation. To appear in Ann. Sc. Norm. Super. Pisa Cl., Preprint at arXiv:1511.04503.
  • Malý, L., and Shanmugalingam, N. (2016). (Under Review). Neumann problem for p-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity. Preprint, arXiv:1609.06808.
  • Malý, L. (2017). (Under Review). Trace and extension theorems for Sobolev-type functions in metric spaces. Preprint, arXiv:1704.06344.
  • Lahti, P., Malý, L., Shanmugalingam, N., and Speight, G. (2017). (Under Review). Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient. Preprint, arXiv:1706.07505.

Presentations & Lectures

Invited Presentations

  • (06/17/2015). Sobolev-type embeddings in metric measure spaces via generalized Poincaré inequalities PDEs, Potential Theory, Function Spaces conference, Linköping, Sweden.
  • (06/01/2015). Self-improvement of Poincaré inequalities and lack thereof Workshop on Analysis and Geometry in Metric Spaces, ICMAT, Madrid, Spain.
  • (07/24/2014). Sobolev-type functions on metric spaces: various approaches and their comparison Siegmundsburg Seminar on Analysis & Theoretical Numerics, Siegmundsburg, Germany.
  • (11/22/2013). Regularisering av Newtonska funktioner med hjälp av uppskattningar för svaga normer av maximaloperatorer Fall meeting of the Swedish Mathematical Society, Linköping, Sweden.
  • (11/19/2011). Newtonian spaces based on Banach function lattices Fall meeting of the Swedish Mathematical Society, Linköping, Sweden.
  • (07/18/2009). Calderón-type theorems on Lorentz Lambda and M spaces Siegmundsburg Seminar on Analysis & Theoretical Numerics, Siegmundsburg, Germany.
  • (03/12/2016). Trace and extension theorems for BV and Sobolev functions in metric spaces The 6th Ohio River Analysis Meeting, University of Kentucky, Lexington, KY, USA.
  • (03/25/2017). Neumann problem for p-Laplace equation in metric spaces The 7th Ohio River Analysis Meeting, University of Cincinnati, Cincinnati, OH, USA.
  • (07/08/2016). Trace and extension theorems for BV and Sobolev functions in metric spaces Function Spaces, Differential Operators and Nonlinear Analysis 2016, Charles University in Prague, Czech Republic.

Poster Presentations

  • Malý, Lukáš (04/08/2017). Besov Spaces and Trace Classes of Sobolev Functions in Metric Spaces Informal Analysis Seminar: Differentiation in finite & infinite dimensions (Kent State University), Kent, OH, USA. [Link]

Colloquia

  • (12/10/2014). Sobolev-type spaces based on linear lattices of measurable functions in metric spaces: existence of minimal gradients. Jyväskylä Analysis Seminar, University of Jyväskylä, Finland.
  • (04/23/2014). Regularity of Newtonian functions: quasi-continuity and continuity. The Prague Seminar on Function Spaces, Academy of Sciences of the Czech Republic, Prague.
  • (03/19/2014). Sobolev-type functions in metric spaces. Regularization by Lipschitz truncations vs. the Newtonian approach. The Prague Seminar on Function Spaces, Academy of Sciences of the Czech Republic, Prague.
  • (11/19/2013). Regularization of Newton–Sobolev functions via weak boundedness of maximal operators. “Evolutionary Problems” program seminar, Institute Mittag-Leffler, Stockholm, Sweden.
  • (12/08/2010). Calderón-type theorems. Mathematical Colloquium, Linköping University, Sweden.
  • (11/26/2010). Newtonian spaces. Research seminar “Function Spaces”, Friedrich-Schiller-Universität Jena, Germany.
  • (10/14/2010). Introduction to rearrangement-invariant spaces. Analysis Seminar, Linköping University, Sweden.
  • (05/25/2016). Trace and extension theorems for BV and Sobolev functions in metric spaces. Mathematical Colloquium, Linköping University, Sweden.

Experience & Service

Work Experience

  • 07-2007 to 06-2009, Junior Programmer, Ness Czech, s.r.o., Prague, Czech Republic.
  • 07-2009 to 05-2010, Experienced Application Software Engineer, NESS Czech, s.r.o., Prague, Czech Republic.
  • 08-2010 to 06-2014, PhD Student, Dept. of Mathematics, Linköping University, Sweden.
  • 07-2014 to 09-2014, Assistant Lecturer, Dept. of Mathematics, Linköping University, Sweden.
  • 10-2014 to 08-2015, Postdoctoral Researcher, Dept. of Mathematics & Statistics, University of Jyväskylä, Finland.

Service

  • Peer Review/Referee, Publicacions Matemàtiques
  • Peer Review/Referee, Czechoslovak Mathematical Journal
  • Peer Review/Referee, Conformal Geometry and Dynamics
  • Peer Review/Referee, Conference proceedings: “Calculus of Variations and PDEs” Banach Center Publications , 2012
  • Peer Review/Referee, Revista Matemática Complutense
  • Peer Review/Referee, Constructive Approximation
  • Peer Review/Referee, Analysis and Geometry in Metric Spaces
  • Reviewer, Mathematical Reviews (AMS)
  • Peer Review/Referee, Journal of Inequalities and Applications
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