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. Calculus of Variations and PDE 63 (2024), article no. 219. (doi link) - 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.