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Prof. Kazuhiro Takimoto  ( Hiroshima University, Japan )

2008 - 01 - 16 (Wed.)
16:10 - 17:00
308, Mathematics Research Center Building (ori. New Math. Bldg.)

In the early 20th century, Rad\'{o} proved the following theorem:\textit{Let $f$ be a continuous complex-valued function in a domain $\Omega \subset \mathbb{C}$. If $f$ is analytic in $\Omega \setminus f^{-1}(0)$, then $f$ is analytic in the whole domain $\Omega$.} That is, a level set is always removable for continuous analytic functions. In this talk, we study the removability of a level set for solutions to general \textit{fully nonlinear} elliptic or parabolic equations. Moreover, we also give some results relevant to Rad\'{o} type theorems in the talk.