Nodal sets of Dirichlet eigenfunctions in quasiconvex Lipschitz domains
Analysis of PDEs
2023-03-06 v1
Abstract
We introduce the class of quasiconvex Lipschitz domains, which covers both and convex domains, to the study of boundary unique continuation for elliptic operators. In particular, we prove the 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.
Keywords
Cite
@article{arxiv.2303.02046,
title = {Nodal sets of Dirichlet eigenfunctions in quasiconvex Lipschitz domains},
author = {Jiuyi Zhu and Jinping Zhuge},
journal= {arXiv preprint arXiv:2303.02046},
year = {2023}
}
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41 pages