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A quantitative Carleman estimate for second-order elliptic operators
Published online by Cambridge University Press: 27 December 2018
Abstract
We prove a Carleman estimate for elliptic second-order partial differential expressions with Lipschitz continuous coefficients. The Carleman estimate is valid for any complex-valued function u ∈ W2,2 with support in a punctured ball of arbitrary radius. The novelty of this Carleman estimate is that we establish an explicit dependence on the Lipschitz and ellipticity constants, the dimension of the space and the radius of the ball. In particular, we provide a uniform and quantitative bound on the weight function for a class of elliptic operators given explicitly in terms of ellipticity and Lipschitz constant.
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- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 4 , August 2019 , pp. 915 - 938
- Copyright
- Copyright © Royal Society of Edinburgh 2018
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