Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates
Abstract
We consider heat operators on a convex domain $Ω$, with a critically singular potential that diverges as the inverse square of the distance to the boundary of $Ω$. We establish a general boundary controllability result for such operators in all dimensions, in particular providing the first such result in more than one spatial dimension. The key step in the proof is a novel global Carleman estimate that captures both the appropriate boundary conditions and the $H^1$-energy for this problem. The estimate is derived by combining two intermediate Carleman inequalities with distinct and carefully constructed weights involving non-smooth powers of the boundary distance.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Analysis & PDE
- Publisher
- Mathematical Sciences Publishers
- Volume
- 19
- Issue
- 2
- Pages
- 241–280
- Publication date
- 22 January 2026
- Language
- EN