A quantitative Carleman estimate for second-order elliptic operators (CROSBI ID 274707)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Nakić, Ivica ; Rose, Christian ; Tautenhahn, Martin
engleski
A quantitative Carleman estimate for second-order elliptic operators
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.
Carleman estimate ; Second order elliptic differential operator ; Explicit weight function
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Podaci o izdanju
149 (4)
2019.
915-938
objavljeno
0308-2105
1473-7124
10.1017/prm.2018.55