Koike Shigeaki, Professor 
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Research field



Theory of viscosity solutions for fully nonlinear partial differential equations, and its applications.


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Research topics of interested 


Fully nonlinear elliptic/parabolic partial differential equations, in particular,
the theory of viscosity solutions and its applications. My recent interests are
(1) regularity theory of Lp viscosity solutions, (2) fractional Laplace operators, (3) quasilinear equations.

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Advice on Research 

Theory of viscosity solutions is a counter part of theory of weak solutions in the distribution sense. Therefore, it is recommended to know (at least to have an interest of) both of them in order to establish a unified theory which has never been existed before. If you would succeed, you could be a pioneer in the world.
To be more realistic, I request you to learn carefully advanced calculus and Lebesgue integration. If possible, knowledge of geometry or probability would help you a lot in the future.

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One word 

God lives in the details.

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