Panu Lahti's research page

E-mail:
HTML5 Icon

HTML5 Icon

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)
  • Fine potential theory for p=1
  • Lower semicontinuity of functionals of linear growth

Recently I have mostly worked on extending results of fine potential theory from the case p>1 to the case p=1. Such results in the case p=1 seem to be mostly 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 minimization problems and approximation results involving the BV class.

Publications

Preprints

  1. R. Jones, P. Lahti, and N. Shanmugalingam, Modulus of families of sets of finite perimeter and quasiconformal maps between metric spaces of globally Q-bounded geometry, preprint 2018.
  2. P. Lahti, Approximation of BV by SBV functions in metric spaces, preprint 2018.
  3. P. Lahti, Federer's characterization of sets of finite perimeter in metric spaces, preprint 2018.
  4. P. Lahti, The Choquet and Kellogg properties for the fine topology when p=1 in metric spaces, preprint 2017.
  5. P. Lahti, The variational 1-capacity and BV functions with zero boundary values on metric spaces, preprint 2017.
  6. 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.
  7. P. Lahti, Quasiopen sets, bounded variation and lower semicontinuity in metric spaces, preprint 2017.

2018

  1. R. Korte, P. Lahti, X. Li, and N. Shanmugalingam, Notions of Dirichlet problem for functions of least gradient in metric measure spaces, to appear in Revista Matemática Iberoamericana.
  2. P. Lahti, A new Cartan-type property and strict quasicoverings when p=1 in metric spaces, to appear in Ann. Acad. Sci. Fenn. Math.
  3. P. Lahti, Strong approximation of sets of finite perimeter in metric spaces, manuscripta mathematica, March 2018, Volume 155, Issue 3–4, pp 503–522.
  4. P. Lahti, Superminimizers and a weak Cartan property for p=1 in metric spaces, to appear in Journal d'Analyse Mathématique.
  5. 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, to appear in Analysis and Geometry in Metric Spaces.
  6. P. Lahti and N. Shanmugalingam, Trace theorems for functions of bounded variation in metric spaces, to appear in Journal of Functional Analysis.

2017

  1. P. Lahti, A Federer-style characterization of sets of finite perimeter on metric spaces, Calc. Var. Partial Differential Equations, October 2017, 56:150.
  2. P. Lahti, A notion of fine continuity for BV functions on metric spaces, Potential Analysis, February 2017, Volume 46, Issue 2, pp 279–294.
  3. P. Lahti, Strict and pointwise convergence of BV functions in metric spaces, Journal of Mathematical Analysis and Applications, Volume 455, Issue 2, 15 November 2017, Pages 1005-1021.
  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.

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. Partial Differential Equations 55 (2016), no. 3, Art. 70, 23 pp.

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