Research interests
Partial Differential Equations.
- Green's functions and regularity theory for second order pdes
- Boundary value problems for second order elliptic pdes in Lipschitz domains
- Free boundary problems
Publications / Preprints
- The Neumann Green function and scale invariant regularity estimates for elliptic equations
with Neumann data in Lipschitz domains. Joint with Seick Kim. Submitted, arXiv version. - Scale invariant regularity estimates for second order elliptic equations with lower order coefficients
in optimal spaces. Journal de Mathématiques Pures et Appliquées 156 (2021), 179-214. (doi link) - Minimizers for the thin one-phase free boundary problem. Joint with Max Engelstein, Aapo Kauranen, Martí Prats and Yannick Sire. Communications on Pure and Applied Mathematics 74 (2021), no. 9, 1971-2022. (doi link)
- On scale invariant bounds for Green's function for second order elliptic equations with lower order coefficients and applications. Analysis and PDE 14 (2021), no. 1, 251-299. (doi link)
- Boundary value problems in Lipschitz domains for equations with lower order coefficients. Transactions of the AMS 372 (2019), no. 8, 5947-5989. (doi link)
- Green's function for second order elliptic equations with singular lower order coefficients. Joint with Seick Kim. Communications in Partial Differential Equations 44 (2019), no. 3, 228-270. (doi link)
A copy of my PhD thesis is available here, and also on the arXiv.