I am interested in regularity of the motion of a surface by its mean curvature. To show the existence of the surface, we frequently consider the various weak type solution. I mainly study the regularity of these weak solutions, in other word, the weak solution is actual solution or not. Considering the embedding to the Euclid space, the moving surface obeys some nonlinear degenerate parabolic equation. I also study regularity theory for nonlinear partial differential equations, especially degenereta parabolic type.
As my interest, I like not only differential equations but also differential geometry. Actually I study the surface and the curve from the point of partial differential equations, geometrical measure theory. Nowadays, I am interested in mathematical modeling for the evolution of grain boundaries, which is related to the motion of a surface. And I study the mathematical properties of the model.
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