Bounds of Eigenfunction for Some Diffusion Operators
Year: 2024
Type: article
Abstract: In this paper, we consider the $L^{\infty}$ bounds of the eigenfunctions for some diffusion operators. In case of classical Laplace eigenvalue problem $\Delta u = -\lambda u$ with Dirichlet boundary condition, we obtain the polynomial bound which is different from the result derived by heat kernel estimates. We then study the nonlocal dispersal eigenvalue problem $\int_{\Omega} J(x-y) u(y) \, dy - u(x) = -\lambda u(x)$ with bounded domain $\Omega$ and obtain an exponential bound by means of Fourier transform and nonlocal estimates.
Source: Taiwanese Journal of Mathematics
DOI: 10.11650/tjm/241104
Authors: Yan-Hua Xing, Jian-Wen Sun
Institution: Lanzhou University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404622550