Ryosuke Shimizu

activity

20242026

collaborators

5 papers

math.FA2026

Higher-order differentiability of Korevaar--Schoen energy forms and energy measures

Ryosuke Shimizu

In this paper, we investigate the differentiability of Korevaar--Schoen $p$ -energy forms and the associated $p$ -energy measures. We obtain higher-order derivatives by virtue of exp…

math.FA2025

$p$ -Energy forms on fractals: recent progress

Naotaka Kajino, Ryosuke Shimizu

In this article, we survey recent progress on self-similar $p$ -energy forms on self-similar fractals, where $p \in (1, \infty)$ . While for $p = 2$ the notion of such forms coincides wit…

math.FA2024

Characterizations of Sobolev functions via Besov-type energy functionals in fractals

Ryosuke Shimizu

In the spirit of the ground-breaking result of Bourgain--Brezis--Mironescu, we establish some characterizations of Sobolev functions in metric measure spaces including fractals lik…

math.FA2024

Contraction properties and differentiability of $p$ -energy forms with applications to nonlinear potential theory on self-similar sets

Naotaka Kajino, Ryosuke Shimizu

We introduce a new contraction property, which we call the generalized $p$ -contraction property, for $p$ -energy forms as generalizations of many well-known inequalities, such as $p…

math.FA2024

Korevaar-Schoen $p$ -energy forms and associated $p$ -energy measures on fractals

Naotaka Kajino, Ryosuke Shimizu

We construct good $p$ -energy forms on metric measure spaces as pointwise subsequential limits of Besov-type $p$ -energy functionals under certain geometric/analytic conditions. Such…

Higher-order differentiability of Korevaar--Schoen energy forms and energy measures

p-Energy forms on fractals: recent progress

Characterizations of Sobolev functions via Besov-type energy functionals in fractals

Contraction properties and differentiability of p-energy forms with applications to nonlinear potential theory on self-similar sets

Korevaar-Schoen p-energy forms and associated p-energy measures on fractals

$p$ -Energy forms on fractals: recent progress

Contraction properties and differentiability of $p$ -energy forms with applications to nonlinear potential theory on self-similar sets

Korevaar-Schoen $p$ -energy forms and associated $p$ -energy measures on fractals