The Leibniz rule for the Dirichlet and the Neumann Laplacian

Tsukasa Iwabuchi

Type: Article

Publication Date: 2023-03-01

Citations: 2

DOI: https://doi.org/10.2748/tmj.20211112

Abstract

We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half space case, which is related to not only smoothness of functions and but also boundary behavior. The crucial point for the proof is how to handle boundary values of functions and their derivatives.

Locations

Tohoku Mathematical Journal - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (22)

Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+ PDF Chat	Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires	1981	Jean-Michel Bony
+	Hitchhikerʼs guide to the fractional Sobolev spaces	2011	Eleonora Di Nezza Giampiero Palatucci Enrico Valdinoci
+	Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data	1994	Hideo Kozono Masao Yamazaki
+	The Hörmander multiplier theorem for multilinear operators	2011	Loukas Grafakos Zengyan Si
+ PDF Chat	Decay rates of the derivatives of the solutions of the heat equations in the exterior domain of a ball	2007	Kazuhiro Ishige Yoshitsugu Kabeya
+	A Hörmander type multiplier theorem for multilinear operators	2010	Naohito Tomita
+	Commutator estimates and the euler and navier‐stokes equations	1988	Tosio Kato Gustavo Ponce
+ PDF Chat	Plancherel-type estimates and sharp spectral multipliers	2002	Xuan Thinh Duong El Maati Ouhabaz Adam Sikora
+ PDF Chat	Riesz Transforms Outside a Convex Obstacle	2015	Rowan Killip Monica Vişan Xiaoyi Zhang