Upper bounds of nodal sets for solutions of bi-Laplace equations: II
Abstract
We investigate the upper bounds of nodal sets for solutions of bi-Laplace equations without using frequency functions which play an essential role in the study of nodal sets in the celebrated work by Logunov \cite{Lo18}. We obtain some delicate monotonicity and propagation of smallness results by Carleman estimates. A polynomial upper bound for the nodal sets of solutions is obtained.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Spectral Theory in Mathematical Physics
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 4 March 2026
- Language
- EN
- Document type
- Preprint