Isakov, Victor On increasing stability of the continuation for elliptic equations of second order without (pseudo)convexity assumptions. (English) Zbl 1423.35447 Inverse Probl. Imaging 13, No. 5, 983-1006 (2019). Summary: We derive bounds of solutions of the Cauchy problem for general elliptic partial differential equations of second order containing parameter (wave number) \(k\) which are getting nearly Lipschitz for large \( k \). Proofs use energy estimates combined with splitting solutions into low and high frequencies parts, an associated hyperbolic equation and the Fourier-Bros-Iagolnitzer transform to replace the hyperbolic equation with an elliptic equation without parameter \(k\). The results suggest a better resolution in prospecting by various (acoustic, electromagnetic, etc) stationary waves with higher wave numbers without any geometric assumptions on domains and observation sites. Cited in 6 Documents MSC: 35R30 Inverse problems for PDEs 35B60 Continuation and prolongation of solutions to PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation Keywords:Cauchy problem; stability of the continuation; inverse problems; Helmholtz equation; Fourier transform PDFBibTeX XMLCite \textit{V. Isakov}, Inverse Probl. Imaging 13, No. 5, 983--1006 (2019; Zbl 1423.35447) Full Text: DOI