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• W2895579990 abstract "In this article, we study a model problem featuring a Levy process in a domain with semi-transparent boundary by considering the following perturbed fractional Laplacian operator [mathscr{L}_{b,q} := (-Delta)^t + (-Delta)_{Omega}^{s/2} b (-Delta)_Omega^{s/2} + q, quad 0<s<t<1] on a bounded Lipschitz domain $Omega subset mathbb{R}^n$. While the non-locality of the fraction Laplacian $(-Delta)^t$ depends on entire $mathbb{R}^n$, in its non-local perturbation the non-locality depends on the domain $Omega$ through the regional fractional Laplacian term $(-Delta)^{s/2}_{Omega}$ and $b$ exhibits the semi-transparency of the process. We analyze the well-posedness of the model and certain qualitative property like unique continuation property, Runge approximation scheme considering its regional non-local perturbation. Then we move into studying the inverse problem and find that by knowing the corresponding Dirichlet to Neumann map (D-N map) of $mathscr{L}_{b,c}$ on the exterior domain $mathbb{R}^n setminus Omega$, it is possible to determine the lower order perturbations `$b$',`$q$' in $Omega$. We also discuss the recovery of `$b$', `$q$' from a single measurement and its limitations." @default.
• W2895579990 created "2018-10-12" @default.
• W2895579990 creator A5057222649 @default.
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• W2895579990 date "2018-10-08" @default.
• W2895579990 modified "2023-09-27" @default.
• W2895579990 title "Inverse Problem for Fractional-Laplacian with Lower Order Non-local Perturbations" @default.
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• W2895579990 doi "https://doi.org/10.13140/rg.2.2.15643.52000" @default.
• W2895579990 hasPublicationYear "2018" @default.
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