Mixed problems for pluriparabolic equations
type: Item
instance of: scholarly article
title: Mixed problems for pluriparabolic equations
zbMATH Open document ID: 0633.35084
author: Reiko Sakamoto
published in: Journal of Mathematics of Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: The author considers linear partial differential operators with smooth coefficients in \({\mathbb{R}}_ t\times {\mathbb{R}}^ n_ x\), of the type \(P=\sum c_{k\lambda}(t,x)D^ k_ tD^{\lambda}_ x\) where \(k,\lambda =(\lambda_ 1,...,\lambda_ n)\) in the sum run over the set \(\{k+\sum^{n}_{j-1}\lambda_ j/p_ j\leq m\}\), for \(p_ 1,...,p_ n\) given with \(p_ 1=...=p_ s=1\), \(p_ j>1\) for \(j=s+1,...,n\) (one assumes \(s\geq 1).\) Under suitable assumptions of the symbol of P, a priori estimates are proved for the solutions of mixed problems, with Cauchy data at \(t=0\) and boundary conditions at \(x_ 1=0\).
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 4030113
zbMATH Keywords: linear
zbMATH Keywords: operators
zbMATH Keywords: smooth coefficients
zbMATH Keywords: a priori estimates
zbMATH Keywords: mixed problems
zbMATH Keywords: Cauchy data
reviewed by: Luigi Rodino
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520878
OpenAlex ID: W1566389051
DOI: 10.1215/KJM/1250520878
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description: scientific article; zbMATH DE number 4030113