A note on Sobolev type inequalities in two independent variables
type: Item
instance of: scholarly article
title: A note on Sobolev type inequalities in two independent variables
zbMATH Open document ID: 0613.26013
DOI: 10.1016/0022-247X(87)90348-9
author: B. G. Pachpatte
published in: Journal of Mathematical Analysis and Applications
publication date: 1987-01-01T00:00:00Z
review text: The inequality \[ \iint^{\infty}_{-\infty}u^ 4dx dy\leq (\alpha /2)(\iint^{\infty}_{-\infty}u^ 2dx dy)(\iint^{\infty}_{- \infty}| \text{grad} u|^ 2dx dy), \] where u(x,y) is a smooth function of compact support and \(\alpha\) is a constant, is known as Sobolev's inequality. The author establishes some new inequalities of this type. The proofs are quite elementary and the results yield in the special cases some known inequalities of Sobolev type.
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 3991819
zbMATH Keywords: integral inequalities
zbMATH Keywords: functions of two independent variables
zbMATH Keywords: inequalities of Sobolev type
reviewed by: Ioan Raşa
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3991819