1 citations · 2 across the 10 of their papers we have counts for
18 papers
Some quasilinear minimization problems involving Hardy potentials
Futoshi Takahashi, Kota Urabe
In this note, we consider several quasiliniear minimization problems involving various Hardy type potentials for functions in with weighted mean zero. We prove that th…
Nondegeneracy of the entire solution for the -Laplace Liouville equation
Futoshi Takahashi
In this note, we prove the nondegenracy of the explicit finite-mass solution to the -Laplace Liouville equation on the whole space, which is recently shown to be unique up to sc…
On eigenvalue problems involving the critical Hardy potential and Sobolev type inequalities with logarithmic weights in two dimensions
Megumi Sano, Futoshi Takahashi
We consider the two-dimensional eigenvalue problem for the Laplacian with the Neumann boundary condition involving the critical Hardy potential. We prove the existence of the secon…
Another approach to the equality case of the sharp logarithmic Sobolev inequality
Filomena Feo, Futoshi Takahashi
In this note, we characterize the equality case of the sharp -Euclidean logarithmic Sobolev inequality with monomial weights, exploiting the idea by Bobkov and Ledoux \cite{Bo…
Critical Hardy inequality on the half-space via the harmonic transplantation
Megumi Sano, Futoshi Takahashi
We prove a critical Hardy inequality on the half-space by using the harmonic transplantation. Also we give an improvement of the subcritical Hardy inequality on the half-space, whi…
Applications of -harmonic transplantation for functional inequalities involving a Finsler norm
Sadaf Habibi, Futoshi Takahashi
In this paper, we prove several inequalities such as Sobolev, Poincaré, logarithmic Sobolev, which involve a general norm with accurate information of extremals, and are valid for…