| Abstract: |
| In this talk, I will introduce a recent proof for the existence of the steady-states of a large class of stationary radiative transfer equations in a $C^1$ convex bounded domain. The main difficulty in proving existence of solutions is to obtain compactness of the sequence of integrals along lines that appear in several exponential terms. Currently available averaging lemmas do not seem to provide sufficient compactness that we require, and I will introduce our new compactness result suitable to deal with such a non-local operator containing integrals on a line segment. |
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