arXiv subjects

Yoshinori Furuto

Publications and source records attributed to Yoshinori Furuto.

3 recordsLinked to original sources

arXiv2026

Higher-order derivative estimates for the parabolic Lamé system on a smooth bounded domain

We consider the parabolic Lamé system on a bounded domain. We focus on two types of inequalities for higher-order derivatives of solutions. The first is related to an $L^p$-$L^p$ estimate locally in time in the Lebesgue space setting, which includes the endpoint cases $p=1$ and $p=\infty$. The second concerns an equivalent norm of Besov spaces by means of the solution of the parabolic Lamé system.

math.AP↗

arXiv2025

Higher-order derivative estimates for the heat equation on a smooth domain

We consider the linear heat equation on a bounded domain and on an exterior domain. We study estimates of any order derivatives of the solution locally in time in the Lebesgue spaces. We give a proof of the estimates in the end-point cases $p = 1, \infty$. We also obtain derivative estimates for the equation with the fractional Dirichlet Laplacian.

math.AP↗

arXiv2024

$L^p$ estimate of the heat equation on a bounded domain

We consider the linear heat equation on a bounded domain. We study estimates of the derivatives, up to the second order, of the solution locally in time in the Lebesgue spaces. We give a self-contained proof of the estimates in the end-point cases $p = 1, \infty$.

math.AP↗