My research interests lie at the interface of Analysis, Partial Differential Equations (PDE), and Geometric Measure Theory (GMT). I am interested in understanding the exact relations between the geometry of sets, the structure of the underlying operators, and the behavior of solutions.
You can find my publications on arxiv.
Here is my Google Scholar page.
The $L^p$ Poisson-Neumann problem and its relation to the Neumann problem (with Joseph Feneuil). 49 pages, arXiv:2406.16735, slides
The $L^p$ regularity problem for parabolic operators (with Martin Dindos, and Jill Pipher). 112 pages, arXiv:2410.23801
Boundary behavior of solutions of elliptic operators in divergence form with a BMO anti-symmetric part (with Jill Pipher).Comm. Partial Differential Equations, 44, no. 2 (2019): 156-204. Journal link, arXiv:1712.06705
$\ell^2$ decoupling in R^2 for curves with vanishing curvature (with Chandan Biswas, Maxim Gilula, Jeremy Schwend, and Yakun Xi). Proc. Amer. Math. Soc. 148, no. 5 (2020): 1987-1997. Journal link, arXiv:1812.04760
The Dirichlet problem for elliptic operators having a BMO anti-symmetric part, (with S. Hofmann, S. Mayboroda, J. Pipher). Math. Ann. (2021) DOI: 10.1007/s00208-021-02219-1. Journal link, arXiv:1908.08587
$L^p$ theory for the square roots and square functions of elliptic operators having a BMO anti-symmetric part (with S. Hofmann, S. Mayboroda, J. Pipher). Math. Z. 301, pages 935–976 (2022). DOI:10.1007/s00209-021-02938-w. Journal link, arXiv:1908.01030
Carleson measure estimates for the Green function, (with G. David and S. Mayboroda). Arch. Ration. Mech. Anal. 243, pages1525–1563 (2022). DOI: 10.1007/s00205-021-01746-0. Journal link, arXiv:2102.09592
Carleson estimates for the Green function on domains with lower dimensional boundaries, (with G. David and S. Mayboroda). J. Funct. Anal. Volume 283, Issue 5 (2022). DOI: 10.1016/j.jfa.2022.109553. Journal link, arXiv:2107.08101
Small $A_\infty$ results for weak Dahlberg-Kenig-Pipher operators in sets with uniformly rectifiable boundaries, (with G. David, S. Mayboroda). Trans. Amer. Math. Soc. (2023) DOI: 10.1090/tran/9004. Journal link, arxiv:2207.13602
Green functions and smooth distances, (with J. Feneuil, S. Mayboroda). Math. Ann. 389 (2024), no.3, 2637–2727. DOI: 10.1007/s00208-023-02715-6. Journal link, arXiv:2211.05318
A Green function characterization of uniformly rectifiable sets of any codimension, (with J. Feneuil). Adv. Math. 430, (2023) Paper No. 109220, DOI: 10.1016/j.aim.2023.109220 Journal link, arXiv:2302.14087, slides
My PhD Thesis: $L^p$ Dirichlet problem for second order elliptic operators having a BMO anti-symmetric part.