Shuntaro Tsubouchi

activity

20202025

most citedLocal Lipschitz bounds for solutions to certain singular elliptic equations involving one-Laplacian

13 citations · 13 across the 7 of their papers we have counts for

collaborators

7 papers

math.AP2025

Gradient continuity for the parabolic $(1, p)$ -Laplace system

Shuntaro Tsubouchi

This paper deals with the parabolic $(1, p)$ -Laplace system, a parabolic system that involves the one-Laplace and $p$ -Laplace operators with $p \in (1, \infty)$ . We aim to prove th…

math.AP2024

Gradient continuity for the parabolic $(1, p)$ -Laplace equation under the subcritical case

Shuntaro Tsubouchi

This paper is concerned with the gradient continuity for the parabolic $(1, p)$ -Laplace equation. In the supercritical case $\frac{2 n}{n + 2} < p < \infty$ , where $n \geq 2$ denotes the s…

math.AP2023

Continuity of the spatial gradient of weak solutions to very singular parabolic equations involving the one-Laplacian

Shuntaro Tsubouchi

We consider weak solutions to very singular parabolic equations involving a one-Laplace-type operator, which is singular and degenerate, and a $p$ -Laplace-type operator with $\frac…

math.AP2022

A weak solution to a perturbed one-Laplace system by $p$ -Laplacian is continuously differentiable

Shuntaro Tsubouchi

In this paper we aim to show continuous differentiability of weak solutions to a one-Laplace system perturbed by $p$ -Laplacian with $1 < p < \infty$ . The main difficulty on this equati…

math.AP2022

Continuous differentiability of a weak solution to very singular elliptic equations involving anisotropic diffusivity

Shuntaro Tsubouchi

In this paper we consider a very singular elliptic equation that involves an anisotropic diffusion operator, including one-Laplacian, and is perturbed by a $p$ -Laplacian-type diffu…

math.AP2021

Continuity of derivatives of a convex solution to a perturbed one-Laplace equation by $p$ -Laplacian

Yoshikazu Giga, Shuntaro Tsubouchi

We consider a one-Laplace equation perturbed by $p$ -Laplacian with $1 < p < \infty$ . We prove that a weak solution is continuously differentiable ( $C^{1}$ ) if it is convex. Note that s…

math.AP2020★ 13 cited

Local Lipschitz bounds for solutions to certain singular elliptic equations involving one-Laplacian

Shuntaro Tsubouchi

In this paper local Lipschitz regularity of weak solutions to certain singular elliptic equations involving one-Laplacian is studied. Equations treated here also contains another w…

Gradient continuity for the parabolic (1,p)-Laplace system

Gradient continuity for the parabolic (1,p)-Laplace equation under the subcritical case

Continuity of the spatial gradient of weak solutions to very singular parabolic equations involving the one-Laplacian

A weak solution to a perturbed one-Laplace system by p-Laplacian is continuously differentiable

Continuous differentiability of a weak solution to very singular elliptic equations involving anisotropic diffusivity

Continuity of derivatives of a convex solution to a perturbed one-Laplace equation by p-Laplacian

Local Lipschitz bounds for solutions to certain singular elliptic equations involving one-Laplacian

Gradient continuity for the parabolic $(1, p)$ -Laplace system

Gradient continuity for the parabolic $(1, p)$ -Laplace equation under the subcritical case

A weak solution to a perturbed one-Laplace system by $p$ -Laplacian is continuously differentiable

Continuity of derivatives of a convex solution to a perturbed one-Laplace equation by $p$ -Laplacian