11 citations · 14 across the 9 of their papers we have counts for
9 papers
Complex harmonic mean
Atsushi Nakayasu
We study the harmonic mean of non-zero complex-valued random variables (complex harmonic mean) and establish several geometric estimates and bounds. In contrast to the classical po…
Stability of metric viscosity solutions under Hausdorff convergence
Shimpei Makida, Atsushi Nakayasu
This study investigated the stability of Hamilton--Jacobi equation on general metric spaces with a perturbation in some whole space. This type of stability appears in the domain pe…
Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces
Qing Liu, Atsushi Nakayasu
We study the convexity preserving property for a class of time-dependent Hamilton-Jacobi equations in a complete geodesic space. Assuming that the Hamiltonian is nondecreasing, we…
Integrability of the derivative of solutions to a singular one-dimensional parabolic problem
Atsushi Nakayasu, Piotr Rybka
We study integrability of the derivative of solutions to a singular one-dimensional parabolic equation with initial data in . In order to avoid additional difficulties we…
Energy solutions to one-dimensional singular parabolic problems with data are viscosity solutions
Atsushi Nakayasu, Piotr Rybka
We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in , which is the energy space. We show existence of solutions in…
Stability properties and large time behavior of viscosity solutions of Hamilton-Jacobi equations on metric spaces
Atsushi Nakayasu, Tokinaga Namba
We investigate asymptotic behaviors of a metric viscosity solution of a Hamilton-Jacobi equation defined on a general metric space in Gangbo-Świȩch sense. Our results include gener…
Two approaches to minimax formula of the additive eigenvalue for quasiconvex Hamiltonians
Atsushi Nakayasu
Two different proofs for an inf-sup type representation formula (minimax formula) of the additive eigenvalues corresponding to first-order Hamilton-Jacobi equations are given for q…
On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems
Nao Hamamuki, Atsushi Nakayasu, Tokinaga Namba
We study a cell problem arising in homogenization for a Hamilton-Jacobi equation whose Hamiltonian is not coercive. We introduce a generalized notion of effective Hamiltonians by a…
On metric viscosity solutions for Hamilton-Jacobi equations of evolution type
Atsushi Nakayasu
This paper studies Hamilton-Jacobi equations of evolution type defined in a general metric space. We give a notion of a solution through optimal principles and establish a unique e…