The Leibniz rule for the Dirichlet and the Neumann Laplacian

Tsukasa Iwabuchi

doi: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.

Citation

Download Citation

Tsukasa Iwabuchi. "The Leibniz rule for the Dirichlet and the Neumann Laplacian." Tohoku Math. J. (2) 75 (1) 67 - 88, 2023. https://doi.org/10.2748/tmj.20211112

Information

Published: 2023

First available in Project Euclid: 24 March 2023

MathSciNet: MR4564843

zbMATH: 07692864

Digital Object Identifier: 10.2748/tmj.20211112

Subjects:

Primary: 46E35

Secondary: 42B35 , 42B37

Keywords: Besov spaces , bilinear estimates , Dirichlet Laplacian , fractional Laplacian , Neumann Laplacian , Sobolev Spaces

Abstract

Citation

Information

KEYWORDS/PHRASES

PUBLICATION TITLE:

PUBLICATION YEARS