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A Convexity Result for Weak Differential Inequalities

Published online by Cambridge University Press:  20 November 2018

S. Zaidman
S. Zaidman*
Affiliation:
Université de Montrèal
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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