Potential Analysis for Sobolev functions

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・The head Investigator, with the help of T. Shimomura, extended the Fatou theorem for Sobolev's monotone functions in the sense of Lebesgue. In relation with Liouville's theorem and Bocher's theorem for harmonic functions, he investigated isolated singularities for polyharmonic functions. Furthermore, he studied Sobolev's function spaces with variable exponent, and extended Sobolev's theorem in the metric space setting.・T.Shibata studied eigen value problem for elliptic partial differential equations.・H.Usami characterized asymptotic forms of positive solutions of second-order quasilinear ordinary differential equations・T.Nagai treated qualitative properties of solutions to a reaction-diffusion equation with advection modelling chemotaxis.・M.Shiba and M.Masumoto studied circularizable domains on Riemann surfaces.・N.Suzuki and M.Nishio extended Bergman space theory for fractional heat equations.・H.Masaoka showed a condition for the existence of positive harmonic functions with finite Dirichlet integral on Riemann surfaces.・T.Shima and M.Furushima studied analytic compactifications in Fano manifolds.・H.Yoshida investigated the behavior of harmonic functions on cones through minimally thin sets.