Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
We present an approach for obtaining quantitative boundary doubling inequalities for elliptic equations with Neumann boundary conditions. Carleman estimates are used to prove three-ball inequalities, which are then used to prove quantitative doubling inequalities, with bootstrapping from the interior to the boundary. This approach is illustrated by its application to the Laplace eigenvalue problem with homogeneous Neumann boundary conditions, where sharp doubling inequalities are recovered.
When then consider a equation with non homogeneous Neumann boundary conditions. By following the approach, we are able to obtain potentially sharp results. Finally, we are able to get an improvement on previously obtained results for the interior doubling inequality of sums of Laplace eigenfunctions.
Date
7-14-2025
Recommended Citation
Dalberg, Jack, "Quantitative Boundary Doubling Estimates for Elliptic Equations" (2025). LSU Doctoral Dissertations. 6861.
https://repository.lsu.edu/gradschool_dissertations/6861
Committee Chair
Zhu, Jiuyi
DOI
10.31390/gradschool_dissertations.6861