Some interpolation inequalities involving Stokes operator and first order derivatives
type: Item
instance of: scholarly article
title: Some interpolation inequalities involving Stokes operator and first order derivatives
zbMATH Open document ID: 0958.35098
DOI: 10.1007/BF01783676
author: P. Maremonti
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2001-03-27T00:00:00Z
review text: The author proves various multiplicative inequalities of the type \[ \|w\|_r \leq c \|P\Delta w\|_p^a \|w\|_q^{1-a}, \tag{1} \] where \(0\leq a \leq 1\), \(P\Delta\) is the Stokes operator in an exterior domain \(\Omega\) in \({\mathbb{R}}^n , n\geq 2\), with sufficiently smooth boundary, and \(\|w\|_p \) is the \(L^p(\Omega)\)-norm. The function \(w\) is taken from appropriate spaces. Analogues of (1), where \(w\) in the left-hand side of (1) is replaced by \(\nabla w\), are also established.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1471595
zbMATH Keywords: Stokes operator
zbMATH Keywords: interpolation inequalities
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1471595