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# AMS Special Session on Regularity of PDEs on Rough Domains

Spring Eastern Sectional Meeting, April 21 - 22, 2018, Northeastern University, Boston, MA

The aim of this session is to focus on regularity of elliptic and parabolic partial differential equations on rough domains. 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, harmonic measure, regularity of free boundaries. Our hope to share the recent developments in this area by bringing together mathematicians from different specialties whose work involves PDEs, harmonic analysis, and Geometric measure theory. 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) -- Max Engelstein (maxe "at" mit.edu). The official link to the AMS web-page for our session is here.

### Important Dates

• Deadline for ALL Abstract Submissions: February 20, 2018
• Please submit abstracts directly at this link (Choose Meeting number 1139 and SS 14A - Special Session on Regularity of PDEs on Rough Domains).
• Session date: April 21 - 22, 2018, Northeastern University, Boston, MA.

### Speakers

• Matthew Badger (University of Connecticut). Title: Two-phase free boundary problem for harmonic measure with Hölder data. Matthew's talk.
• Ariel Barton (University of Arkansas). Title: Extrapolation of well posedness for higher order elliptic systems with rough coefficients.
• Bruno G. Poggi Cevallos (University of Minnesota).Title: Exponential decay estimates for fundamental solutions of Schr\"odinger-type operators.
• Donatella Danielli (Purdue University). Title: Regularity Results for a Penalized Boundary Obstacle Problem. Donatella's talk.
• Blair Davey (City College of New York). Title: How to obtain parabolic theorems from their elliptic counterparts. Blair gave a board talk, related article.
• Joseph Feneuil (University of Minnesota). Title: The Dirichlet problem for sets with higher co-dimensional boundaries.
• Jose Luis Luna Garcia (University of Missouri). Title: Solvability of Elliptic Equations with Lower Order Terms.
• Mariana Smit Vega Garcia (University of Washington). Title: Higher regularity of the free boundary in the parabolic Signorini problem. Mariana's talk.
• Silvia Ghinassi (Stony Brook University). Title: $C^{1,\alpha}$ parametrization and rectifiability. Silvia's talk.
• Steve Hofmann (University of Missouri). Title: Quantitative Rectifiability and absolute continuity of harmonic measure. Steve's talk.
• John Lewis (Univeristy of Kentucky). Title: Note on an Eigenvalue Problem.
• Sean McCurdy (University of Washington). Title: A Tale of Two Approaches.
• Katie Ott (Bates College). Title: The mixed boundary value problem in Lipschitz domains. Katy's talk.
• Luca Spolaor (MIT). Title: Logarithmic Epiperimetric inequality and the regularity of the free-boundary. [This talk was cancelled]
• Andy Vogel (Syracuse University). Title: The Brunn-Minkowski inequality and a Minkowski problem for nonlinear capacity. Andy's talk.
• Bobby Wilson (MIT). Title: Arbitrarily Slowly Decaying Favard Length.
• Zihui Zhao (University of Washington). Title: Elliptic measures and geometric properties of the domains. Zihui's talk.
• Xiaodan Zhou (WPI). Title: Strong Comparison Principle for $p-$harmonic functions in Carnot-Caratheodory spaces. Xiaodan's talk.

Photo Credit: Michael Albanese