Prof. Dr. Simon Blatt

Room 1.026

Hellbrunnerstr. 34

5020 Salzburg, Austria

I hold the position of Associate Professor in the field of Analysis. My research focuses on partial differential equations and the calculus of variations.

I am particularly fascinated by the intricate connections between geometry, topology, and analysis, which manifest in the study of functionals such as Willmore or Helfrich for surfaces, as well as in the exploration of knot energies.

news

Jul 4, 2024	Workshop on nonlinear PDE’s in Salzburg, October 23rd to 25th! Find out more and register here.

selected publications

Journal Articles

2020

The gradient flow of the Möbius energy: \varepsilon-regularity and consequences

Simon Blatt

Analysis & PDE, Apr 2020

Abs DOI

In this article we study the gradient flow of the Möbius energy introduced by O’Hara in 1991. We will show a fundamental \varepsilon-regularity result that allows us to bound the infinity norm of all derivatives for some time if the energy is small on a certain scale. This result enables us to characterize the formation of a singularity in terms of concentrations of energy and allows us to construct a blow-up profile at a possible singularity. This solves one of the open problems listed by Zheng-Xu He. Ruling out blow-ups for planar curves, we will prove that the flow transforms every planar curve into a round circle.

2017

Monotonicity formulas for extrinsic triharmonic maps and the triharmonic Lane–Emden equation

Simon Blatt

Journal of Differential Equations, Apr 2017

Abs DOI

We derive monotonicity formulas and \varepsilon-regularity results for extrinsic triharmonic maps and triharmonic Lane-Emden equations. As an application, we prove partial regularity results for both types of equations in the supercritical regime.

2015

An Analytic Framework for the Supercritical Lane–Emden Equation and its Gradient Flow

Simon Blatt, and Michael Struwe

Int. Math. Res. Not. IMRN, Apr 2015

Abs DOI

The natural setting for the Lane-Emden equation -∆u = |u|^p-2u on a domain Ω⊂\R^n, n\ge 3, for supercritical exponents p>2^*=2n/(n-2) is identified as the space of functions u∈H^1_0∩L^p(Ω) with finite scale-invariant Morrey norms. We show that this Morrey regularity is propagated by the heat flow associated with this equation, and we study the blow-up profiles.