A class of pseudo-differential operators with weight functions and its applications to energy estimates for degenerate elliptic operators
type: Item
instance of: scholarly article
title: A class of pseudo-differential operators with weight functions and its applications to energy estimates for degenerate elliptic operators
zbMATH Open document ID: 0656.35152
author: Reiko Sakamoto
published in: Journal of Mathematics of Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: Pseudo-differential operators with weight functions are very useful tools to deal with partial differential operators with degenerate symbols. These weight functions have some restrictions so that the formal expansions of the products of pseudo-differential operators have their substantial meaning. In this paper, a class of pseudo-differential operators with weight functions is introduced with less restrictions, although their formal expansions have the substantial meaning only for a type of products of pseudo-differential operators. In {\S} 1, a class of pseudo-differential operators is introduced. In {\S} 2, a quasi-parametric is constructed for a pseudo-differential operator belonging to a sub-class, in the same way as by \textit{L. Hörmander} [Proc. Sympos. Pure Math. 10, 138-183 (1967; Zbl 0167.096)]. In {\S} 3 and {\S} 4, some applications on energy estimates are given for a class of elliptic differential operators with a parameter, degenerating on the boundary of a domain.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35J10
zbMATH DE Number: 4071560
zbMATH Keywords: weight functions
zbMATH Keywords: degenerate symbols
zbMATH Keywords: formal expansions
zbMATH Keywords: quasi- parametric
zbMATH Keywords: energy estimates
zbMATH Keywords: operators with a parameter
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520605
OpenAlex ID: W1540674624
DOI: 10.1215/KJM/1250520605
description: scientific article; zbMATH DE number 4071560