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An inverse source problem for the Monge--Ampere equation from large boundary data
Cătălin 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
Cătălin 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
Cătălin 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
Cătălin 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{in…