3 citations · 4 across the 6 of their papers we have counts for
10 papers · 1 filter
Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
Masahiro Ikeda, Megumi Sano, Koichi Taniguchi
We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the radial and the subcritical homogeneous Sobolev spaces $\dot{W}^{1,p}_{0, \te…
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…
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…
Improvements and generalizations of two Hardy type inequalities and their applications to the Rellich type inequalities
Megumi Sano
We give improvements and generalizations of both the classical Hardy inequality and the geometric Hardy inequality based on the divergence theorem. Especially, our improved Hardy t…
Explicit optimal constants of two critical Rellich inequalities for radially symmetric functions
Megumi Sano
We consider two critical Rellich inequalities with singularities at both the origin and the boundary in the higher order critical radial Sobolev spaces , w…
Minimization problem associated with an improved Hardy-Sobolev type inequality
Megumi Sano
We consider the existence and the non-existence of a minimizer of the following minimization problems associated with an improved Hardy-Sobolev type inequality introduced by Ioku.…