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Controllability of
parabolic equations with inverse square infinite potential
wells via global Carleman estimates
Alberto Enciso, Arick Shao and Bruno Vergara |
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Vol. 19 (2026), No. 2, 241–280
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Abstract |
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We consider heat operators on a convex domain , with a critically singular potential that diverges as the inverse square of the distance to the boundary of . 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 new global Carleman estimate with a carefully chosen weight that captures the appropriate boundary conditions, the global geometry of the domain , and the -energy for this problem. The estimate is derived by combining two intermediate Carleman inequalities with distinct and carefully constructed weights involving nonsmooth powers of the boundary distance. |
Keywords
heat equation, controllability, observability, singular
potential Carleman
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Mathematical Subject Classification
Primary: 35-XX
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Milestones
Received: 30 October 2023
Revised: 18 November 2024
Accepted: 6 March 2025
Published: 22 January 2026
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Authors |
| Alberto Enciso | |
| Instituto de Ciencias
Matemáticas Consejo Superior de Investigaciones Científicas Madrid Spain |
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| Arick Shao | |
| School of Mathematical
Sciences Queen Mary University of London London United Kingdom |
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| Bruno Vergara | |
| Department of Mathematics Brown University Providence, RI United States |
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| © 2026 MSP (Mathematical Sciences Publishers). |
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