We introduce the class of quasiconvex Lipschitz domains, which covers both C1 and convex domains, to the study of boundary unique continuation for elliptic operators. In particular, we prove an upper bound of the size of nodal sets for Dirichlet eigenfunctions of general elliptic equations in bounded quasiconvex Lipschitz domains. Our result is new even for Laplace operator in convex domains. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Publication:

ADVANCES IN MATHEMATICS

http://dx.doi.org/10.1016/j.aim.2026.111150

Author:

Jiuyi Zhu

Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

Corresponding authors

Email：zhu@math.lsu.edu

Jinping Zhuge

Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Corresponding authors.

Email：jpzhuge@amss.ac.cn