Personal tools

Theme for TIFR Centre For Applicable Mathematics, Bangalore

You are here: Home / Inverse problems for fractional Laplacian with non-local lower order perturbation

# Inverse problems for fractional Laplacian with non-local lower order perturbation

Dr. Sombuddha Bhattacharya Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong
 Speaker Dr. Sombuddha Bhattacharya Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong Aug 09, 2018 from 04:00 PM to 05:00 PM LH 006 vCal iCal

Abstract:  In this talk I will be presenting a recent work, jointly done with Prof. Gunther Uhlmann and Dr. Tuhin Ghosh, where we consider a non-local inverse problem and determine more than one lower order coefficients from the associate Cauchy data. We consider the following perturbed fractional Laplacian operator

$$(-\Delta)^t + (-\Delta)_{\Omega}^{{s}/{2}} \ b (-\Delta)_{\Omega}^{{s}/{2}} + c, \quad 0<s<t<1$$

on a bounded Lipschitz domain $$\Omega \subset \mathbb{R}^n$$. Apart from the global non-locality in the principal part, our operator exhibits regional non-locality in its lower order regional fractional Laplacian perturbation term $$(-\Delta)^{s/2}_{\Omega}$$.

We find that by knowing the corresponding Dirichlet to Neumann map (D-N map) on the exterior domain $$\mathbb{R}^n \setminus \Omega$$, it is possible to determine the lower order coefficients $$b'$$ ,$$c'$$ in $$\Omega$$. We also discuss the recovery of $$b'$$, $$c$$' from a single measurement and its limitations

Filed under: