3 citations · 4 across the 5 of their papers we have counts for
10 papers
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…
Two limits on Hardy and Sobolev inequalities
Megumi Sano
It is known that classical Hardy and Sobolev inequalities hold when the exponent and the dimension satisfy . In this note, we consider two limits of Hardy a…
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.…