6 papers
The Calderón problem for piecewise polynomial anisotropic conductivities on partitions with many flat faces
CÄtÄlin I. Cârstea, Cătălin I. Cârstea
We prove uniqueness for a finite-dimensional anisotropic Calderón problem in dimensions . The unknown conductivity is a symmetric uniformly elliptic matrix field whose res…
An inverse source problem for the Monge--Ampere equation from large boundary data
CÄtÄlin I. Cârstea, Tuhin Ghosh
We study an inverse source problem for the Monge--Ampere equation \[ \det D^2u=f(x) \] on a bounded smooth uniformly convex domain. In the smooth classical regime, we prove that th…
A note on several inverse problems with generally random coefficients
CÄtÄlin I. Cârstea
We consider several inverse problems for elliptic equations whose coefficients are random, without imposing a special probabilistic structure on the randomness. The main body treat…
Hölder Stability from Exact Uniqueness for Finite-Dimensional Analytic Inverse Problems
CÄtÄlin I. Cârstea
We prove a stability theorem for finite-dimensional analytic inverse problems. Let \(U\subset\R^m\) be an open parameter set, let \(F(p)\) be a boundary measurement operator, and l…
Inverse boundary value problems for certain doubly nonlinear parabolic and elliptic equations
CÄtÄlin I. Cârstea, Tuhin Ghosh
We consider an inverse boundary value problem for the doubly nonlinear parabolic equation \[ ε(x)\partial_t u^m-\nabla\cdot\bigl(γ(x)|\nabla u|^{p-2}\nabla u\bigr)=0 \quad\text{i…
Reconstruction of coefficients in the double phase problem
CÄtÄlin I. Cârstea, Philipp Zimmermann
The main purpose of this article is to reconstruct the nonnegative coefficient in the double phase problem $\mathrm{div}\,(|\nabla u|^{p-2}\nabla u+a|\nabla u|^{q-2}\nabla u)=0…