Inverse problems for elliptic equations with fractional power type nonlinearities
Liimatainen, T., Lin, Y.-H., Salo, M., & Tyni, T. (2022). Inverse problems for elliptic equations with fractional power type nonlinearities. Journal of Differential Equations, 306, 189-219. https://doi.org/10.1016/j.jde.2021.10.015
Julkaistu sarjassa
Journal of Differential EquationsPäivämäärä
2022Oppiaine
Inversio-ongelmien huippuyksikköMatematiikkaCentre of Excellence in Inverse ProblemsMathematicsTekijänoikeudet
© 2022 Elsevier
We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. By using a fractional order adaptation of this method, we show that the results of [24], [23] remain valid for general power type nonlinearities.
Julkaisija
ElsevierISSN Hae Julkaisufoorumista
0022-0396Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/101789930
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Rahoittaja(t)
Suomen AkatemiaRahoitusohjelmat(t)
Akatemiahanke, SA; Huippuyksikkörahoitus, SALisätietoja rahoituksesta
T.L. and M.S. are supported by the Finnish Centre of Excellence in Inverse Modelling and Imaging, Academy of Finland grant 284715, and T.T. by grant 312119. M.S. was also supported by the Academy of Finland (grant 309963) and by the European Research Council under Horizon 2020 (ERC CoG 770924). Y.-H.L. is supported by the Ministry of Science and Technology, Taiwan, under the Columbus Program: MOST-109-2636-M-009-006, MOST-110-2636-M-009- 007. ...Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations
Lassas, Matti; Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko (European Mathematical Society Publishing House, 2021)We study various partial data inverse boundary value problems for the semilinear elliptic equation Δu + a(x, u) = 0 in a domain in Rn by using the higher order linearization technique introduced by Lassas– Liimatainen–Lin–Salo ... -
The Linearized Calderón Problem on Complex Manifolds
Guillarmou, Colin; Salo, Mikko; Tzou, Leo (Springer, 2019)In this note we show that on any compact subdomain of a K¨ahler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to ... -
On some partial data Calderón type problems with mixed boundary conditions
Covi, Giovanni; Rüland, Angkana (Elsevier, 2021)In this article we consider the simultaneous recovery of bulk and boundary potentials in (degenerate) elliptic equations modelling (degenerate) conducting media with inaccessible boundaries. This connects local and nonlocal ... -
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 ... -
On the scientific work of Victor Isakov
Krupchyk, Katya; Salo, Mikko; Uhlmann, Gunther; Wang, Jenn-Nan (American Institute of Mathematical Sciences (AIMS), 2022)
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.