With emphasis on uniformly rectifiable domains

Files related to my talks at the Fabes-Riviere Symposium, April 2011

This is the set of lecture notes for my talks at the symposium.

Singular integrals and elliptic boundary problems on rough domains.

Click here for  “Singular Integrals and Elliptic Boundary Problems on Regular Semmes-Kenig-Toro Domains,” with Steve Hofmann and Marius Mitrea.  IMRN 2010 (2010), 2567-2865.

The talks focused on material in this paper.

Click here for “Short Course on Pseudodifferential Operators” Four Lectures at MSRI, Sept. 2008.  Chapter III contains material on analysis on Lipschitz domains, uniformly rectifiable domains, and SKT domains.

Click here for “Remarks on the Gauss-Green theorem.”  These notes discuss various forms of the Gauss-Green theorem developed in the IMRN paper listed above.  These results, essential for the IMRN paper, also have the potential for wider applicability.

Further work on analysis on uniformly rectifiable domains.

Click here for “Cauchy integrals, Calderon projectors, and Toeplitz operators on uniformly rectifiable domains,” with I. Mitrea and M. Mitrea, Adv. in Math. 268 (2015), 666-757.

Click here for a set of lecture notes on this paper, prepared for a talk at the University of Michigan, Dec. 2014.

Click here for “Multidimensional Riemann-Hilbert problems on domains with uniformly rectifiable interfaces,”with I. Mitrea and M. Mitrea, Preprint, 2015.

Click here for “Multidimensional Toeplitz operators with locally sectorial symbols,” Comm. PDE 42 (2017), 1322-1334.

Work on somewhat less rough domains, possibly the maximal class allowing for a symbol calculus.

Click here for “Symbol calculus for operators of layer potential type on Lipschitz surfaces with vmo normals, and related pseudodifferential operator calculus,” with S. Hofmann and M. Mitrea, Analysis and PDE 8 (2015), 115-181.