How to determine convexity of functional I am a rookie to functional and calculus of variation. I want to know whether there exists any   sufficient condition for convexity of a functional besides the definition. Actually for function, one sufficient condition for convexity is that its Hessian matrix is positive definite. Can this conclusion be extended to the functional case?
In addition, are there any books involving these? Thanks.

Have a look at:

*

*Bruce van Brunt - The Calculus of Variations, paragraph 10.7

*I.M. Gelfand and S.V. Fomin - Calculus of Cariations, Chapter 5

