Zongyuan Li

Zongyuan Li

he/him

Preprints

  1. Asymptotic expansions for harmonic functions at conical boundary points. (With D. Kriventsov) To appear in Rev. Mat. Iberoam. arxiv

  2. Liouville theorems for conformally invariant fully nonlinear equations. I. (With B.Z. Chu and Y.Y. Li) Submitted. arxiv

  3. On the fully nonlinear Yamabe problem with constant boundary mean curvature. I. (With B.Z. Chu and Y.Y. Li) Submitted. arxiv

  4. Liouville Theorem with Boundary Conditions from Chern-Gauss-Bonnet Formula. (With B.Z. Chu and Y.Y. Li) Submitted. arxiv

Papers

  1. Classical solutions of oblique derivative problem in nonsmooth domains with mean Dini coefficients. (With H. Dong) Trans. Amer. Math. Soc., 373(7) : 4975-4997, 2020. arxiv, Journal

  2. The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions. (With H. Dong) Comm. Partial Differential Equations, 46(3):470–497, 2021. arxiv, Journal

  3. Optimal Regularity for a Dirichlet-Conormal Problem in Reifenberg Flat Domain. (With J. Choi and H. Dong) Appl. Math. Optim., 83(3):1547-1583, 2021. arxiv, Journal

  4. The conormal and Robin boundary value problems in nonsmooth domains satisfying a measure condition. (With H. Dong) J. Funct. Anal., 281(9):Paper No. 109167, 32, 2021. arxiv, Journal

  5. Norm inflation for the Boussinesq system. (With W. Wang) Discrete Contin. Dyn. Syst. Ser. B, 26(10):5449-5463, 2021. arxiv, Journal

  6. On the \(W^2_p\) estimate for oblique derivative problems of second order elliptic equations. (With H. Dong) Int. Math. Res. Not. IMRN, (5):3602-3635, 2022. arxiv, Journal.

  7. Optimal regularity of mixed Dirichlet conormal boundary value problems for parabolic operators. (With J. Choi and H. Dong) SIAM J. Math. Anal., 54(2):1393-1427, 2022. arxiv, Journal

  8. The Dirichlet-conormal problem for the heat equation with inhomogeneous boundary conditions. (With H. Dong) Adv. Math., , 411: Paper No. 108777, 2022. arxiv, Journal

  9. Quantitative unique continuation for Robin boundary value problems on C1,1 domains. (With W. Wang) Indiana Univ. Math. J., 72(4):1429–1460, 2023. arxiv, Journal

  10. Mixed boundary value problems for parabolic equations in Sobolev spaces with mixed-norms. (With J. Choi and H. Dong) Calc. Var. Partial Differential Equations., 62(1): Paper No. 5, 2023. arxiv, Journal

  11. Asymptotics of harmonic functions in the absence of monotonicity formulas. In Extended Abstracts, 2021/2022, Trends in Mathematics, vol 3, pages 125 – 131. Birkhäuser, 2024. arxiv, Book Chapter

  12. On the uniqueness of variable coefficient Schr"odinger equations. (With S. Federico and X. Yu) Commun. Contemp. Math., 27(3), 2025. arxiv, Journal

  13. Unique continuation on Robin problems with non-smooth potentials. J. Funct. Anal., 288(6):Paper No. 110811, 2025. arxiv, Journal