| Abstract: |
| In this talk I will formulate an inverse source problem for the prescribed mean curvature equation (PMC)
\begin{equation*}
\nabla\cdot\left[\frac{\nabla u}{\left(1+|\nabla u|^2\right)^{1/2}}\right] = H(x)\quad\text{in }\Omega
\end{equation*}
for a smooth bounded set $\Omega\subset R^2$. The question is if from measurements done on the boundary $\partial\Omega$ one can determine the mean curvature $H$ in $\Omega$. The talk is based on joint work with Tony Liimatainen (https://arxiv.org/abs/2509.22078) and we show that it is indeed possible to recover $H$. The proof relies on the higher order linearization method and asymptotical analysis in an integral identity using complex geometric optics solutions from the work of Guillarmou and Tzou in 2011. |
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