Zobrazeno 1 - 10
of 15
pro vyhledávání: '"Tony Liimatainen"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 12 (2024)
We investigate an inverse boundary value problem of determination of a nonlinear law for reaction-diffusion processes, which are modeled by general form semilinear parabolic equations. We do not assume that any solutions to these equations are known
Externí odkaz:
https://doaj.org/article/fc3e83e8c3394567a860cca88aa515bf
In this paper we consider determining a minimal surface embedded in a Riemannian manifold $\Sigma\times \mathbb{R}$. We show that if $\Sigma$ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Ne
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b1238d9b03efe70cc9d9ff74ee5bb6b5
https://doi.org/10.2139/ssrn.4354195
https://doi.org/10.2139/ssrn.4354195
We consider the recovery of a potential associated with a semi-linear wave equation on Rn+1, n > 1. We show that an unknown potential a(x, t) of the wave equation ???u + aum = 0 can be recovered in a H & ouml;lder stable way from the map u|onnx[0,T]
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b6dccd148dffb3c00ce0469d9bdf13a
http://hdl.handle.net/10138/350037
http://hdl.handle.net/10138/350037
Publikováno v:
Journal de Mathématiques Pures et Appliquées
We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equation
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2c4177c2244ebc11cc55ab870df23b70
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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3ccc486a38ee53c28e27e9cb414ccbbd
http://arxiv.org/abs/2012.04944
http://arxiv.org/abs/2012.04944
In this article we study the linearized anisotropic Calderon problem. In a compact manifold with boundary, this problem amounts to showing that products of harmonic functions form a complete set. Assuming that the manifold is transversally anisotropi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3140bcb4f8b2489a769c064a02741f57
http://urn.fi/URN:NBN:fi:jyu-202012187301
http://urn.fi/URN:NBN:fi:jyu-202012187301
We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime $(M,g)$ with an unknown metric $g$. We consider measurements done in a neighbourhood $V\subset M$ of a timelike path $\mu$ that connects a point $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::98fd21a566cfd31533beda8e1f899222
Publikováno v:
Mathematische Annalen
We introduce a new approach to the anisotropic Calder\'on problem, based on a map called Poisson embedding that identifies the points of a Riemannian manifold with distributions on its boundary. We give a new uniqueness result for a large class of Ca
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8ac7d324ccc875d4b472551bc3396ff7
Autor:
Tony Liimatainen, Lauri Oksanen
Publikováno v:
Inverse Problems & Imaging. 16:467
We construct counterexamples to inverse problems for the wave operator on domains in $\mathbb{R}^{n+1}$, $n \ge 2$, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which are formu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5959e57e9d809963b7efff1c961da50a
https://doi.org/10.3934/ipi.2021058
https://doi.org/10.3934/ipi.2021058
Publikováno v:
Communications in Analysis and Geometry. 25(2):395-430
We show that on any Riemannian manifold with H¨older continuous metric tensor, there exists a p-harmonic coordinate system near any point. When p = n this leads to a useful gauge condition for regularity results in conformal geometry. As application
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fef4389d42476b073f9e36511aadf531
http://juuli.fi/Record/0285099917
http://juuli.fi/Record/0285099917