WebbA Carleman estimate is an L2 -weighted estimate for solutions to system (1.1), and is stated as follows: by choosing a weight function ϕ = ϕ (x, t), there exist constants C > 0 and s0 > 0 such that Z Z Z 3 2 2sϕ 2 2sϕ s u e dxdt ≤ C Lu e dxdt + C ∇x,t u 2e2sϕ dΣ (1.3) Ω×I Ω×I ∂ (Ω×I) for all s ≥ s0 . WebbThe proofs are based on a Carleman estimate where the weight function depends on H. 1. Introduction and main results Let Ω ⊂ Rn be a bounded domain with smooth boundary and H = (h1 , ..., hn ) ∈ (C 1 (Ω))n . Let (x·y) and x denote the scalar product of x, y ∈ Rn and the norm of x ∈ Rn , respectively.

Carleman estimates and some inverse problems for the coupled ...

Webbinteresting feature of his bound is that, for A normal, it reduces to the usual estimate (zI −A)−1 ≤ 1 d(z,σ(A)). His proof relies on an adaptation of finite-dimensional arguments which can be traced to work of Henrici from the early sixties [Hen]. The estimate of Dechevski and Persson, obtained by different methods, does not rely WebbCarleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations Loc H. Nguyen∗ Michael V. Klibanov† Abstract The main … polyester partner crossword clue

Matlab program method of computing Carleman estimates and …

Webb16 mars 2012 · The so-called Carleman estimate is a class of weighted energy estimates which is in connection with (stochastic) differential operators. As far as we know, the … Webb3 dec. 2024 · This is a classical Carleman estimate and we can prove similarly, for example, to lemma 7.1 in or theorem 3.2 in by keeping all the boundary integrals of v(⋅, t … WebbFor the isotropic stationary Lamé system with variable coefficients equipped with the Dirichlet or surface stress boundary condition, we obtain a Carleman estimate such that (i) the right hand side is estimated in a weighted L 2-space and (ii) the estimate includes nonhomogeneous surface displacement or surface stress. Using this estimate we … shang land development corp