Hölder stability of quantitative photoacoustic tomography based on partial data.

Abstract: 

The talk is related to  the inverse problem of reconstructing the diffusion and absorption coefficients of the diffusion equation from internal data in photo-acoustic imaging. I will show that the problem is Hölder stable in subregions close to the boundary where the internal information is available. The Hölder exponent  converges to a positive constant independent of the subregion as the subregion contracts towards the boundary. I will also present several numerical tests  that illustrate  the theoretical results.