Motohiro Sobajima

most citedAn elementary proof of asymptotic behavior of solutions of

u " = V u

4 citations · 4 across the 2 of their papers we have counts for

collaborators

5 papers

math.AP2024

Domain characterization for Schrödinger operators with sub-quadratic singularity

Giorgio Metafune, Motohiro Sobajima

We characterize the domain of the Schrödinger operators $S = - Δ + c ∣ x ∣^{- α}$ in $L^{p} (R^{N})$ , with $0 < α < 2$ and $c \in R$ . When $α p < N$ , the domain characterization is ess…

math.AP2023★ 1 cited

Optimal decay for one-dimensional damped wave equations with potentials via a variant of Nash inequality

Motohiro Sobajima

The optimality of decay properties of the one-dimensional damped wave equations with potentials belonging to a certain class is discussed. The typical ingredient is a variant of Na…

math.AP2023

Lifespan estimates for semilinear damped wave equation in a two-dimensional exterior domain

Masahiro Ikeda, Motohiro Sobajima, Koichi Taniguchi +1

Lifespan estimates for semilinear damped wave equations of the form $\partial_{t}^{2} u - Δ u + \partial_{t} u = ∣ u ∣^{p}$ in a two dimensional exterior domain endowed with the Dirichlet boundary co…

math.AP2014★ 4 cited

An elementary proof of asymptotic behavior of solutions of $u " = V u$

G. Metafune, M. Sobajima

We provide an elementary proof of the asymptotic behavior of solutions of second order differential equations.

math.AP2014

Scale invariant elliptic operators with singular coefficients

G. Metafune, N. Okazawa, M. Sobajima +1

We show that a realization of the operator $L = ∣ x ∣^{α} Δ + c ∣ x ∣^{α - 1} \frac{x}{∣ x ∣} \cdot \nabla - b ∣ x ∣^{α - 2}$ generates a semigroup in $L^{p} (R^{N})$ if and only if $D_c=b+(N-2+c)^2/4…