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arXiv · 2112.04457

Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates

Alberto Enciso·Arick Shao·Bruno Vergara
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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.

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Alberto Enciso, Arick Shao, Bruno Vergara. 2025-03-10. Controllability of parabolic equations with inverse square infinite potential wells via global Carleman estimates. https://doi.org/10.2140/apde.2026.19.241

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