Naslov
A quantitative Carleman estimate for second-order elliptic operators

Autori
Nakić, Ivica ; Rose, Christian ; Tautenhahn, Martin

Izvornik
Proceedings. Section A. Mathematics (Edinburgh) (0308-2105) 149 (2019), 4; 915-938

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Carleman estimate ; Second order elliptic differential operator ; Explicit weight function

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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