Zobrazeno 1 - 10
of 79
pro vyhledávání: '"inversio-ongelmat"'
Publikováno v:
Communications in Analysis and Geometry. 30:1121-1184
We consider a conformally invariant version of the Calderón problem, where the objective is to determine the conformal class of a Riemannian manifold with boundary from the Dirichlet-to-Neumann map for the conformal Laplacian. The main result states
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0c07cc0ec1577ebf76c1a692b000f6ac
https://doi.org/10.4310/cag.2022.v30.n5.a6
https://doi.org/10.4310/cag.2022.v30.n5.a6
Autor:
Salo, Mikko, Tzou, Leo
Publikováno v:
Proceedings of the American Mathematical Society.
We consider the inverse problem of determining a potential in a semilinear elliptic equation from the knowledge of the Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that the potential is uniquely determined by the Dirichlet-to-Neum
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd308a71360202c66c07926fd7b70764
https://doi.org/10.1090/proc/16255
https://doi.org/10.1090/proc/16255
Autor:
Joonas Ilmavirta, Keijo Mönkkönen
We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::93e1dc9195c3db06dec3a014b0c2be62
http://urn.fi/URN:NBN:fi:jyu-202303062015
http://urn.fi/URN:NBN:fi:jyu-202303062015
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
Autor:
Hjørdis Amanda Schlüter, Mikko Salo
The aim of hybrid inverse problems such as Acousto-Electric Tomography or Current Density Imaging is the reconstruction of the electrical conductivity in a domain that can only be accessed from its exterior. In the inversion procedure, the solutions
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a4375414507a02df69b36e17219ec950
http://arxiv.org/abs/2207.03849
http://arxiv.org/abs/2207.03849
Autor:
Brander, Tommi, Siltakoski, Jarkko
Publikováno v:
Documenta Mathematica
We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d34bfd10effaf8b43620c95d9c8383ae
https://doi.org/10.4171/dm/827
https://doi.org/10.4171/dm/827
Autor:
Keijo Mönkkönen, Joonas Ilmavirta
Publikováno v:
SIAM Journal on Mathematical Analysis. 53:3002-3015
If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray tra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::62e09d34af79ee7e3ba69c7222f11e8a
https://doi.org/10.1137/20m1344779
https://doi.org/10.1137/20m1344779
Publikováno v:
SIAM Journal on Mathematical Analysis. 53:7062-7080
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 equation were established by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::253fd1d5fb7a6e6a6b2ff60b8c19a8a0
https://doi.org/10.1137/21m1402169
https://doi.org/10.1137/21m1402169
Autor:
Janne Nurminen
In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential $q$ in $L^{n/2+\varepsilon}$, $\varepsilon>0$, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the results fr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a5e89a07201fec720ad511567b4e7079
http://arxiv.org/abs/2206.04866
http://arxiv.org/abs/2206.04866