Samankaltainen aineisto
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Optimality of Increasing Stability for an Inverse Boundary Value Problem
Kow, Pu-Zhao; Uhlmann, Gunther; Wang, Jenn-Nan (Society for Industrial & Applied Mathematics (SIAM), 2021)In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for the Schrödinger equation. The rigorous justification of increasing stability for the IBVP for the Schrödinger ... -
Fixed domain approaches in shape optimization problems with Dirichlet boundary conditions
Neittaanmäki, Pekka; Pennanen, Anssi; Tiba, Dan (IOP Publishing, 2009)Fixed domain methods have well-known advantages in the solution of variable domain problems including inverse interface problems. This paper examines two new control approaches to optimal design problems governed by general ... -
The higher order fractional Calderón problem for linear local operators : Uniqueness
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse; Uhlmann, Gunther (Elsevier, 2022)We study an inverse problem for the fractional Schrödinger equation (FSE) with a local perturbation by a linear partial differential operator (PDO) of order smaller than the one of the fractional Laplacian. We show that ... -
Unique continuation property and Poincaré inequality for higher order fractional Laplacians with applications in inverse problems
Covi, Giovanni; Mönkkönen, Keijo; Railo, Jesse (American Institute of Mathematical Sciences (AIMS), 2021)We prove a unique continuation property for the fractional Laplacian (−Δ)s when s∈(−n/2,∞)∖Z where n≥1. In addition, we study Poincaré-type inequalities for the operator (−Δ)s when s≥0. We apply the results to show that ... -
An inverse problem for the fractional Schrödinger equation in a magnetic field
Covi, Giovanni (Institute of Physics, 2020)This paper shows global uniqueness in an inverse problem for a fractional magnetic Schrödinger equation (FMSE): an unknown electromagnetic field in a bounded domain is uniquely determined up to a natural gauge by infinitely ...
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