Work

Quantitative uniqueness for bi-Laplace equations with potentials

Year: 2026

Type: preprint

Abstract: We study quantitative unique continuation for bi-Laplace equations \[Δ^{2}u+V(x)u=0 \] by introducing some new weighted frequency functions. We establish quantitative three-ball inequalities and vanishing-order bounds for bounded and Hölder continuous potentials. Three-ball inequalities are built on rescaling invariant weighted frequency functions. The vanishing order results are shown by related, but different weighted frequency functions.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2608.08866

Authors: Teng, Long, Wang, Zhiwei, Zhu, Jiuyi

Institutions: Louisiana State University, University of Science and Technology of China

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7202213604

Cites: 2

Cited by: 1

Related to: 10