Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Railo, Jesse"'
Autor:
Jathar, Shubham R., Railo, Jesse
The article surveys inverse problems related to the twisted geodesic flows on Riemannian manifolds with boundary, focusing on the generalized ray transforms, tensor tomography, and rigidity problems. The twisted geodesic flow generalizes the usual ge
Externí odkaz:
http://arxiv.org/abs/2410.04911
Autor:
Jathar, Shubham R., Railo, Jesse
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
Comment: 7 pages, 11 figures, accepted survey article
Comment: 7 pages, 11 figures, accepted survey article
Externí odkaz:
http://arxiv.org/abs/2410.04908
Autor:
Railo, Jesse
Publikováno v:
J Fourier Anal Appl 30, 59 (2024)
We study Sobolev $H^s(\mathbb{R}^n)$, $s \in \mathbb{R}$, stability of the Fourier phase problem to recover $f$ from the knowledge of $|\hat{f}|$ with an additional Bessel potential $H^{t,p}(\mathbb{R}^n)$ a priori estimate when $t \in \mathbb{R}$ an
Externí odkaz:
http://arxiv.org/abs/2404.13329
We study the injectivity of the matrix attenuated and nonabelian ray transforms on compact surfaces with boundary for nontrapping $\lambda$-geodesic flows and the general linear group of invertible complex matrices. We generalize the loop group facto
Externí odkaz:
http://arxiv.org/abs/2312.06023
Publikováno v:
The Journal of Geometric Analysis 34, 212 (2024)
We prove a uniqueness result for the broken ray transform acting on the sums of functions and $1$-forms on surfaces in the presence of an external force and a reflecting obstacle. We assume that the considered twisted geodesic flows have nonpositive
Externí odkaz:
http://arxiv.org/abs/2306.17604
We investigate global uniqueness for an inverse problem for a nonlocal diffusion equation on domains that are bounded in one direction. The coefficients are assumed to be unknown and isotropic on the entire space. We first show that the partial exter
Externí odkaz:
http://arxiv.org/abs/2211.07781
Publikováno v:
SIAM Journal on Mathematical Analysis (2024), vol. 56 (2), pp. 2456-2487
We study the stability of an inverse problem for the fractional conductivity equation on bounded smooth domains. We obtain a logarithmic stability estimate for the inverse problem under suitable a priori bounds on the globally defined conductivities.
Externí odkaz:
http://arxiv.org/abs/2210.01875
Autor:
Railo, Jesse, Zimmermann, Philipp
Publikováno v:
Nonlinear Analysis 239 (2024), article no. 113418
We characterize partial data uniqueness for the inverse fractional conductivity problem with $H^{s,n/s}$ regularity assumptions in all dimensions. This extends the earlier results for $H^{2s,\frac{n}{2s}}\cap H^s$ conductivities by Covi and the autho
Externí odkaz:
http://arxiv.org/abs/2208.11465
Publikováno v:
Calc. Var. 62, 130 (2023)
This article investigates nonlocal, fully nonlinear generalizations of the classical biharmonic operator $(-\Delta)^2$. These fractional $p$-biharmonic operators appear naturally in the variational characterization of the optimal fractional Poincar\'
Externí odkaz:
http://arxiv.org/abs/2208.09528
We prove \emph{global} uniqueness for an inverse problem for the fractional conductivity equation on domains that are bounded in one direction. The conductivities are assumed to be isotropic and nontrivial in the exterior of the domain, while the dat
Externí odkaz:
http://arxiv.org/abs/2204.04325