Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-14T13:54:52.005Z Has data issue: false hasContentIssue false
  • English
  • Français

A Convexity Result for Weak Differential Inequalities

Published online by Cambridge University Press:  20 November 2018

S. Zaidman
S. Zaidman*
Affiliation:
Université de Montrèal
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we present a natural “weak” form of a certain convexity estimate for evolution inequalities as given in Agmon-Nirenberg’s paper [1], p. 139 (see also A. Friedman [2], Theorem 4.2 and 4.3). Our proof will follow that given in [1] and [2] with the natural modifications due to the enlargement of the class of solutions which are taken into account.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 2 , 01 June 1976 , pp. 235 - 244
Copyright
Copyright © Canadian Mathematical Society 1976

Footnotes

(1)

This research is supported by a grant of the National Research Council, Canada.

References

1. Agmon, S. and Nirenberg, L., Properties of solutions of ordinary differential equations in Banach space. Comm. Pure Appl. Math., May 1963, pp. 121–239.CrossRefGoogle Scholar
2. Friedman, A., Partial Differential Equations. Holt, Rinehart and Winston, Inc., 1969.Google Scholar
3. Yosida, K., Functional Analysis. Springer-Verlag, 1965.Google Scholar
4. Zaidman, S., Remarks on weak solution of differential equations in Banach spaces. Boll. U.M.I. (4) 9 (1974), pp. 638–643.Google Scholar