arXiv subjects

Hiroki Miyakawa

Publications and source records attributed to Hiroki Miyakawa.

3 recordsLinked to original sources

arXiv2025

Existence of distributional solutions to degenerate elliptic systems for locally integrable forcing

This paper presents an existence result and maximal regularity estimates for distributional solutions to degenerate/singular elliptic systems of $p$-Laplacian type with absorption and (prescribed) locally integrable forcing posed in (possibly unbounded) Lipschitz domains. In particular, the forcing terms may not belong to the dual space of an energy space, e.g., $W^{1,p}_{\rm loc}$, which is necessary for the existence of weak (or energy) solutions of class $W^{1,p}_{\rm loc}$. The method of a proof relies on both local energy estimates and a relative truncation technique developed by Bulíček and Schwarzacher (Calc. Var. PDEs in 2016), where the bounded domain case is studied for (globally) integrable forcing.

math.AP↗

arXiv2022

Applications of a duality between generalized trigonometric and hyperbolic functions II

Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of Wilker-type inequalities, Huygens-type inequalities, and (relaxed) Cusa-Huygens-type inequalities for the generalized functions. In addition, multiple- and double-angle formulas not previously obtained are also given.

math.CA↗

arXiv2020

Applications of a duality between generalized trigonometric and hyperbolic functions

It is shown that generalized trigonometric functions and generalized hyperbolic functions can be transformed from each other. As an application of this transformation, a number of properties for one immediately lead to the corresponding properties for the other. In this way, Mitrinović-Adamović-type inequalities, multiple-angle formulas, and double-angle formulas for both can be produced.

math.CA↗