9 citations · 20 across the 18 of their papers we have counts for
19 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…
Asymptotic behavior of least energy solutions to the Finsler Lane-Emden problem with large exponents
Sadaf Habibi, Futoshi Takahashi
In this paper we are concerned with the least energy solutions to the Lane-Emden problem driven by an anisotropic operator, so-called the Finsler -Laplacian, on a bounded domain…
A curl-free improvement of the Rellich-Hardy inequality with weight
Naoki Hamamoto, Futoshi Takahashi
We consider the best constant in the Rellich-Hardy inequality (with a radial power weight) for curl-free vector fields on , originally found by Tertikas-Zographopoulo…
Sharp Logarithmic Sobolev and related inequalities with monomial weights
Filomena Feo, Futoshi Takahashi
We derive a sharp Logarithmic Sobolev inequality with monomial weights starting from a sharp Sobolev inequality with monomial weights. Several related inequalities such as Shannon…
Sharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl
Naoki Hamamoto, Futoshi Takahashi
In this paper, we prove Hardy-Leray inequality for three-dimensional solenoidal (i.e., divergence-free) fields with the best constant. To derive the best constant, we impose the ax…
A note on radial solutions to the critical Lane-Emden equation with a variable coefficient
Daisuke Naimen, Futoshi Takahashi
In this note, we consider the following problem, \begin{equation*} \begin{cases} -Δu=(1+g(x))u^{\frac{N+2}{N-2}},\ u>0\text{ in }B,\\ u=0\text{ on }\partial B, \end{cases} \end{equ…
Sharp Hardy-Leray and Rellich-Leray inequalities for curl-free vector fields
Naoki Hamamoto, Futoshi Takahashi
In this paper, we prove Hardy-Leray and Rellich-Leray inequalities for curl-free vector fields with sharp constants. This complements the former work by Costin-Maz'ya \cite{Costin-…
Finsler Hardy-Kato's inequality
Angelo Alvino, Adele Ferone, Anna Mercaldo +2
We prove an improved version of the trace-Hardy inequality, so-called Kato's inequality, on the half-space in Finsler context. The resulting inequality extends the former one obtai…
Finsler Hardy inequalities
A. Mercaldo, M. Sano, F. Takahashi
In this paper we present a unified simple approach to anisotropic Hardy inequalities in various settings. We consider Hardy inequalities which involve a Finsler distance from a poi…
Weighted Hardy's inequality in a limiting case and the perturbed Kolmogorov equation
Megumi Sano, Futoshi Takahashi
In this paper, we show a weighted Hardy inequality in a limiting case for functions in weighted Sobolev spaces with respect to an invariant measure. We also prove that the constant…
Hardy's inequality in a limiting case on general bounded domains
Jaeyoung Byeon, Futoshi Takahashi
In this paper, we study Hardy's inequality in a limiting case: for func…
On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem
Van Hoang Nguyen, Futoshi Takahashi
In this paper, we establish a weighted Trudinger-Moser type inequality with the full Sobolev norm constraint on the whole Euclidean space. Main tool is the singular Trudinger-Moser…
Critical and subcritical fractional Trudinger-Moser type inequalities on
Futoshi Takahashi
In this paper, we are concerned with the critical and subcritical Trudinger-Moser type inequalities for functions in a fractional Sobolev space on the whole real line.…
On the location of two blow up points on an annulus for the mean field equation
M. Grossi, F. Takahashi
We consider the mean field equation on two-dimensional annular domains, and prove that if and are two blow up points of a blowing-up solution sequence of the equation, then…