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## AMS Special Session on Regularity Theory of PDEs and Calculus of Variations on Domains with Rough Boundaries

Spring Eastern Sectional Meeting, April 13 - 14, 2019, University of Connecticut Hartford, Hartford, CT

This session is focused on the regularity of elliptic and parabolic partial differential equations, and calculus of variations on domains with rough boundaries. In particular, we hope to focus on problems involving solvability of the second and higher order elliptic differential equations and systems in non-smooth media, free boundary problems, harmonic/elliptic/non-linear elliptic measures, analysis and PDEs on uniformly rectifiable sets, and regularity of free boundaries. Our hope is to share the recent developments in this area by bringing together mathematicians from different specialties whose work involves PDEs, harmonic analysis, geometric measure theory, and calculus of variations. We hope to particularly focus on graduate students and early career mathematicians in order to help to start future collaborations that will renew and refresh research in this fundamental area of analysis and PDEs.

Organizers: Murat Akman (murat.akman "at" uconn.edu) -- Zihui Zhao (zzhao "at" ias.edu). The official link to the AMS web-page for our session is here.

### Important Dates

• Deadline for ALL Abstract Submissions: February 5th, 2019
(Choose Meeting number 1148 and SS 5A - Special Session on Regularity Theory of PDEs and Calculus of Variations on Domains with Rough Boundaries).
• Session date: April 13 - 14, 2019, University of Connecticut Hartford, Hartford, CT.

### Speakers

• Simon Bortz (University of Washington). Title of the talk: (Vanishing) Chord arc domains and elliptic measure.
• Donatella Danielli (Purdue University). Title of the talk: The obstacle problem for the fractional heat equation: properties of the free boundary.
• Nicholas Edelen (MIT). Title of the talk: A global bound for the singular set of area-minimizing hypersurfaces.
• Joseph Feneuil (Temple University). Title of the talk: The Dirichlet problem for sets with higher co-dimensional boundaries.
• Mariana Smit Vega Garcia (Western Washington University). Title of the talk: The fractional unstable obstacle problem.
• Silvia Ghinassi (Stony Brook University). Title of the talk: Higher order rectifiability via Reifenberg theorems for sets and measures.
• Max Goering (University of Washington). Title of the talk: Non-local curvatures and the geometry of measures.
• Steve Hofmann (University of Missouri). Title of the talk: A criterion for quantitative absolute continuity of caloric measure.
• Ben Jaye (Clemson University). Title of the talk: Regularity properties of Calderon-Zygmund operators and associated extremal problems.
• John Lewis (University of Kentucky). Title of the talk: Note on an eigenvalue problem with applications to a Minkowski type regularity problem.
• Chema Martell (ICMAT, Spain). Title of the talk: Elliptic operators on rough domains.
• Sean McCurdy (University of Washington). Title of the talk: Unique Continuation on Convex Domains.
• Tomas Merchán (Kent State University). Title of the talk: On the relation between $L^2$ boundedness and existence of principal value integral for a Calderón-Zygmund operator.
• Robin Neumayer (Northwestern University). Title of the talk: Strong-form stability for the Sobolev inequality.
• Phuc Cong Nguyen (Louisiana State University).Title of the talk: Pointwise gradient estimates for a class of singular quasilinear equation with measure data.
• Dali Nimer (University of Chicago). Title of the talk: Singularities of Uniformly Asymptotically Doubling measures.
• Kaj Nyström (Uppsala University). Title of the talk: Boundary estimates for the Kolmogorov-Fokker-Planck operator.
• Bruno Poggi (University of Minnesota). Title of the talk: Carleson perturbations of elliptic operators on domains with higher co-dimensional boundaries.
• Luca Spolaor (MIT).
• Andy Vogel (Syracuse University). Title of the talk: Brunn-Minkowski inequality and Minkowski problem for $p$-Laplace like equations in $\mathbb{R}^n$ for $p\geq n$.
• Yijing Wu (The University of Texas at Austin). Title of the talk: A non-local one-phase free boundary problem from obstacle to cavitation.
• Hui Yu (Columbia University). Title of the talk: Regularity of optimal transport between planar convex domains.