Geodesic
A Convexity Result for Weak Differential Inequalities
Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 235-244

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Zaidman, S. A Convexity Result for Weak Differential Inequalities. Canadian mathematical bulletin, Tome 19 (1976) no. 2, pp. 235-244. doi: 10.4153/CMB-1976-037-4
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[1] 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. Google Scholar | DOI

[2] 2. Friedman, A., Partial Differential Equations. Holt, Rinehart and Winston, Inc., 1969. Google Scholar

[3] 3. Yosida, K., Functional Analysis. Springer-Verlag, 1965. Google Scholar

[4] 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

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