Regularity Theory of PDEs & Calculus of Variations on Domains with Rough Boundaries

The session

PDEs, geometry & variations

This session focused on elliptic and parabolic PDEs and the calculus of variations on domains with rough boundaries. Topics included second- and higher-order elliptic equations and systems in non-smooth media, free boundary problems, harmonic and nonlinear elliptic measures, analysis on uniformly rectifiable sets, and regularity of free boundaries.

The meeting connected researchers in PDEs, harmonic analysis, geometric measure theory and the calculus of variations, with a particular focus on graduate students, early-career mathematicians and future collaborations.

Organisers: Murat Akman and Zihui Zhao.

Programme

Speakers, slides & articles

• Simon Bortz

  University of Washington

  (Vanishing) Chord arc domains and elliptic measure.

  Board talk · Related articles: Article 1 ↗ · Article 2 ↗

• Donatella Danielli

  Purdue University

  The obstacle problem for the fractional heat equation: properties of the free boundary.

  Talk slides ↗

• Nicholas Edelen

  MIT

  A global bound for the singular set of area-minimizing hypersurfaces.

  Board talk · Related article ↗

• Joseph Feneuil

  Temple University

  The Dirichlet problem for sets with higher co-dimensional boundaries.

  Board talk

• Mariana Smit Vega Garcia

  Western Washington University

  The fractional unstable obstacle problem.

  Talk slides ↗

• Silvia Ghinassi

  Stony Brook University

  Higher order rectifiability via Reifenberg theorems for sets and measures.

• Max Goering

  University of Washington

  Non-local curvatures and the geometry of measures.

  Talk slides ↗

• Steve Hofmann

  University of Missouri

  A criterion for quantitative absolute continuity of caloric measure.

  Board talk · Related articles: Article 1 ↗ · Article 2 ↗

• Ben Jaye

  Clemson University

  Regularity properties of Calderon-Zygmund operators and associated extremal problems.

• John Lewis

  University of Kentucky

  Note on an eigenvalue problem with applications to a Minkowski type regularity problem.

• Chema Martell

  ICMAT, Spain

  Elliptic operators on rough domains.

  Talk slides ↗

• Sean McCurdy

  University of Washington

  Unique Continuation on Convex Domains.

• Tomas Merchán

  Kent State University

  On the relation between L² boundedness and existence of principal value integral for a Calderón-Zygmund operator.

• Robin Neumayer

  Northwestern University

  Strong-form stability for the Sobolev inequality.

  Talk slides ↗

• Phuc Cong Nguyen

  Louisiana State University

  Pointwise gradient estimates for a class of singular quasilinear equation with measure data.

• Dali Nimer

  University of Chicago

  Singularities of Uniformly Asymptotically Doubling measures.

• Kaj Nyström

  Uppsala University

  Boundary estimates for the Kolmogorov-Fokker-Planck operator.

• Bruno Poggi

  University of Minnesota

  Carleson perturbations of elliptic operators on domains with higher co-dimensional boundaries.

• Andy Vogel

  Syracuse University

  Brunn-Minkowski inequality and Minkowski problem for p-Laplace like equations in ℝⁿ for p ≥ n.

  Talk slides ↗

• Yijing Wu

  The University of Texas at Austin

  A non-local one-phase free boundary problem from obstacle to cavitation.

  Board talk · Related article ↗

• Hui Yu

  Columbia University

  Regularity of optimal transport between planar convex domains.

  Talk slides ↗