14 citations · 85 across the 11 of their papers we have counts for
11 papers
Unique determination of coefficients and kernel in nonlocal porous medium equations with absorption term
Yi-Hsuan Lin, Philipp Zimmermann
The main purpose of this article is the study of an inverse problem for nonlocal porous medium equations (NPMEs) with a linear absorption term. More concretely, we show that under…
Inverse problem for a nonlocal diffuse optical tomography equation
Philipp Zimmermann
In this article a nonlocal analogue of an inverse problem in diffuse optical tomography is considered. We show that whenever one has given two pairs of diffusion and absorption coe…
Determining coefficients for a fractional -Laplace equation from exterior measurements
Manas Kar, Yi-Hsuan Lin, Philipp Zimmermann
We consider an inverse problem of determining the coefficients of a fractional -Laplace equation in the exterior domain. Assuming suitable local regularity of the coefficients…
The Calderón problem for a nonlocal diffusion equation with time-dependent coefficients
Yi-Hsuan Lin, Jesse Railo, Philipp Zimmermann
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 a…
Stability estimates for the inverse fractional conductivity problem
Giovanni Covi, Jesse Railo, Teemu Tyni +1
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…
Low regularity theory for the inverse fractional conductivity problem
Jesse Railo, Philipp Zimmermann
We characterize partial data uniqueness for the inverse fractional conductivity problem with regularity assumptions in all dimensions. This extends the earlier results…
The fractional -biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems
Manas Kar, Jesse Railo, Philipp Zimmermann
This article investigates nonlocal, fully nonlinear generalizations of the classical biharmonic operator . These fractional -biharmonic operators appear naturally in the…
The global inverse fractional conductivity problem
Giovanni Covi, Jesse Railo, Philipp Zimmermann
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…
Fractional Calderón problems and Poincaré inequalities on unbounded domains
Jesse Railo, Philipp Zimmermann
We generalize many recent uniqueness results on the fractional Calderón problem to cover the cases of all domains with nonempty exterior. The highlight of our work is the character…
Counterexamples to uniqueness in the inverse fractional conductivity problem with partial data
Jesse Railo, Philipp Zimmermann
We construct counterexamples for the partial data inverse problem for the fractional conductivity equation in all dimensions on general bounded open sets. In particular, we show th…
Space-time error estimates for deep neural network approximations for differential equations
Philipp Grohs, Fabian Hornung, Arnulf Jentzen +1
Over the last few years deep artificial neural networks (DNNs) have very successfully been used in numerical simulations for a wide variety of computational problems including comp…