Studies on the applications of the theory of viscosity solutions to some singular perturbation problems

Katsuyuki石井研究了Bence，Merriman和Osher提出的平均曲率运动的数值算法，得到了如下结果：1.给出了由该算法导出平均曲率流方程的收敛性证明。(This是与后藤洋子和小川孝义的合作作品。）2.在平均曲率平滑运动的情况下，给出了该算法的收敛速度。我还表明了最优性的情况下，一个圆的曲率演变。丸尾研二半线性退化椭圆偏微分方程的平面。3.假设方程的系数是径向对称的，证明了在无穷远处的某些增长条件下，连续粘性解是径向对称的。Kageyama Yasuo得到了修正的伯恩斯坦多项式的收敛速度和一些性质

Katsuyuki Ishii studied a numerical algorithm for motion by mean curvature, which is proposed by Bence, Merriman and Osher and obtained the following results1.I gave a proof of convergence showing how the mean curvature flow equation is derived from this algorithm. (This is a joint work with Yoko Goto and Takayoshi Ogawa.)2.I obtained the rate of convergence of this algorithm in the case of smoth motion by mean curvature. I also showed the optimality in the case of a circle evolving by curvature.Kenji Maruo studied semilinear degenerate elliptic partial differential equations in the plane. He obtained the following3.Assuming that the coefficients of the equation are radially symmetric, he proved that, under some growth conditions at infinity, the continuous viscosity solutions are radially symmetricYasuo Kageyama obtained the rate of convergence and some properties of modified Bernstein polynomials