| 研究実績の概要 |
The first project studies the discontinuous eikonal equation in metric measure spaces. Besides uniqueness and existence results for the associated Dirichlet boundary, we obtain the regularity of the unique solution under suitable assumptions.
The second project is concerned with a PDE approach to horizontally quasiconvex functions in the Heisenberg group based on a nonlinear second order elliptic operator. We discuss sufficient conditions and necessary conditions for upper semicontinuous, h-quasiconvex functions in terms of the viscosity subsolution to the associated elliptic equation.
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