Back to Search
Start Over
Some Quantitative Properties of Solutions to the Buckling Type Equation
- Publication Year :
- 2023
-
Abstract
- In this paper, we investigate the quantitative unique continuation, propagation of smallness and measure bounds of nodal sets of solutions to the Buckling type equation $\triangle^2u+\lambda\triangle u-k^2u=0$ in a bounded analytic domain $\Omega\subseteq\mathbb{R}^n$ with the homogeneous boundary conditions $u=0$ and $\frac{\partial u}{\partial\nu}=0$ on $\partial\Omega$, where $\lambda,\ k$ are nonnegative real constants, and $\nu$ is the outer unit normal vector on $\partial\Omega$. We obtain that, the upper bounds for the maximal vanishing order of $u$ and the $n-1$ dimensional Hausdorff measure of the nodal set of $u$ are both $C(\sqrt{\lambda}+\sqrt{k}+1)$, where $C$ is a positive constant only depending on $n$ and $\Omega$. Moreover, we also give a quantitative result of the propagation of smallness of $u$.
- Subjects :
- Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2307.15854
- Document Type :
- Working Paper