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Mathematical Journal of Ibaraki University
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Mathematical Journal of Ibaraki University Vol. 48(2016)

Liouville type theorem on conformal mapping for indefinite metrics associate with ultra-hyperbolic equations

Katsunori Shimomura

Released: October 15, 2016

p.1-18

In [4], we proved that any transformation which preserves solutions of the wave equation is a similarity, an inversion, or a Bateman transformation. This paper gives a generalization of the results to ultra-hyperbolic type equations.

A uniqueness theorem for semistar operations on 1-dimensional Prüfer domains

Ryûki Matsuda

Released: October 15, 2016

p.19-25

We study star and semistar operations on 1-dimensional Prüfer domains D. We prove a uniqueness theorem for y-representations of sigma operations on D.

Presemistar operations on integral domains

Akira Okabe

Released: October 15, 2016

p.27-43

In this paper we introduce the notion of presemistar operation and enlarge the theory of semistar operation to the theory of presemistar operation.

Remarks on Kato's inequality when ∆_pu is a measure

Xiaojing Liu, Toshio Horiuchi

Released: October 15, 2016

p.45-61

Let Ω be a bounded domain of R^N(N ≥ 1). In this article, we shall study Kato's inequality when ∆_pu is a measure, where ∆_pu denotes a p-Laplace operator with 1 < p < ∞. The classical Kato's inequality for a Laplacian asserts that given any function u ∈ L¹_loc(Ω) such that ∆u ∈ L¹_loc(Ω), then ∆(u⁺) is a Radon measure and the following holds: ∆(u⁺) ≥ χ_[_{u ≥}_0]∆u in D^′(Ω). Our main result extends Kato's inequality to the case where ∆_pu is a Radon measures on Ω. We also establish the inverse maximum principle for ∆_p.

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Volume And Issue List
Mathematical Journal of Ibaraki University

Mathematical Journal of Ibaraki University Vol. 48(2016)

Liouville type theorem on conformal mapping for indefinite metrics associate with ultra-hyperbolic equations

A uniqueness theorem for semistar operations on 1-dimensional Prüfer domains

Presemistar operations on integral domains

Remarks on Kato's inequality when ∆_pu is a measure

System Maintenance

Announcement From J-STAGE

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Volume And Issue List Mathematical Journal of Ibaraki University

Mathematical Journal of Ibaraki University Vol. 48(2016)

Liouville type theorem on conformal mapping for indefinite metrics associate with ultra-hyperbolic equations

A uniqueness theorem for semistar operations on 1-dimensional Prüfer domains

Presemistar operations on integral domains

Remarks on Kato's inequality when ∆pu is a measure

System Maintenance

Announcement From J-STAGE

Journal Tools

Share this Title

Volume And Issue List
Mathematical Journal of Ibaraki University

Remarks on Kato's inequality when ∆_pu is a measure