Panu Lahti's research page

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Affiliation

I am a postdoctoral researcher at the Department of Mathematics and Statistics of the University of Jyväskylä. I did my doctoral studies at Aalto University and I collaborate mainly with members of the Nonlinear PDE Research Group.

Research interests

  • Analysis on metric measure spaces
  • Functions of bounded variation (BV functions)
  • Lower semicontinuity of functionals of linear growth
  • Fine potential theory for p=1

Recently I have mostly studied (semi)continuity properties of BV functions and functions of least gradient, and related superminimizers. Some such properties are new even in Euclidean spaces, but it is natural to study them in the more general setting of a metric space equipped with a doubling measure and supporting a Poincaré inequality. I am also interested in extending results of fine potential theory from the case p>1 to the case p=1.

Publications

Preprints

  1. P. Lahti, The variational 1-capacity and BV functions with zero boundary values on metric spaces, preprint 2017.
  2. P. Lahti, L. Malý, and N. Shanmugalingam, An analog of the Neumann problem for the 1-Laplace equation in the metric setting: existence, boundary regularity, and stability, preprint 2017.
  3. P. Lahti, L. Malý, G. Speight, and N. Shanmugalingam, Domains in metric measure spaces with boundary of positive mean curvature, and the Dirichlet problem for functions of least gradient, preprint 2017.
  4. P. Lahti, Superminimizers and a weak Cartan property for p=1 in metric spaces, preprint 2017.
  5. P. Lahti, Quasiopen sets, bounded variation and lower semicontinuity in metric spaces, preprint 2017.
  6. R. Korte, P. Lahti, X. Li, and N. Shanmugalingam, Notions of Dirichlet problem for functions of least gradient in metric measure spaces, preprint 2016.
  7. P. Lahti and N. Shanmugalingam, Trace theorems for functions of bounded variation in metric spaces, preprint 2015.

2017

  1. P. Lahti, A Federer-style characterization of sets of finite perimeter on metric spaces, to appear in Calc. Var. Partial Differential Equations.
  2. P. Lahti, Strict and pointwise convergence of BV functions in metric spaces, to appear in Journal of Mathematical Analysis and Applications.
  3. P. Lahti, Strong approximation of sets of finite perimeter in metric spaces, to appear in manuscripta mathematica.
  4. P. Lahti and N. Shanmugalingam, Fine properties and a notion of quasicontinuity for BV functions on metric spaces, Journal de Mathématiques Pures et Appliquées, Volume 107, Issue 2, February 2017, Pages 150–182.
  5. P. Lahti, A notion of fine continuity for BV functions on metric spaces, Potential Analysis, February 2017, Volume 46, Issue 2, pp 279–294.

2016

  1. H. Hakkarainen, J. Kinnunen, P. Lahti, and P. Lehtelä, Relaxation and Integral Representation for Functionals of Linear Growth on Metric Measure spaces, Anal. Geom. Metr. Spaces 4 (2016), Art. 13.
  2. J. Kristensen and P. Lahti, Lower semicontinuity for an integral functional in BV, Calc. Var. (2016) 55:70.

2015

  1. H. Hakkarainen, J. Kinnunen and P. Lahti, Regularity of minimizers of the area functional in metric spaces, Adv. Calc. Var. 8 (2015), no. 1, 55-68.
  2. H. Hakkarainen, R. Korte, P. Lahti, and N. Shanmugalingam, Stability and continuity of functions of least gradient, Anal. Geom. Metr. Spaces 3 (2015), 123-139.
  3. R. Korte, P. Lahti, and N. Shanmugalingam, Semmes family of curves and a characterization of functions of bounded variation in terms of curves, Calc. Var. Partial Differential Equations 54 (2015), no. 2, 1393-1424.
  4. P. Lahti, Extensions and traces of functions of bounded variation on metric spaces, Journal of Mathematical Analysis and Applications, Volume 423, Issue 1, 1 March 2015, Pages 521-537.

2014

  1. R. Korte and P. Lahti, Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces, Annales de l'Institut Henri Poincaré Non Linear Analysis, Volume 31, Issue 1, January-February 2014, Pages 129-154.
  2. P. Lahti and H. Tuominen, A pointwise characterization of functions of bounded variation on metric spaces, Ric. Mat. 63 (2014), no. 1, 47-57.

Theses