Potential theoretic properties of the gradient of a convex function on a functional space

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Abstract
In the previous paper [11], introducing the notions of potentials and of capacity associated with a convex function Φ given on a regular functional space we discussed potential theoretic properties of the gradient ∇Φ which were originally introduced and studied by Calvert [5] for a class of nonlinear monotone operators in Sobolev spaces. For example: (i)The modulus contraction operates. (ii)The principle of lower envelope holds. (iii)The domination principle holds. (iv)The contraction Tk onto the real interval [0, k] (k > 0) operates. (v)The strong principle of lower envelope holds. (vi)The complete maximum principle holds.

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