Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs by Pierluigi Colli Angelo Favini Elisabetta Rocca Giulio Schimperna & Jürgen Sprekels

Author:Pierluigi Colli, Angelo Favini, Elisabetta Rocca, Giulio Schimperna & Jürgen Sprekels
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2.for any z ∈ D(ϕ), there is a sequence {z n } in V such that

2 Main Theorems

We begin with the precise formulation of our problem (P; f, u 0).

We suppose that the duality mapping F: V → V ∗ is strongly monotone, more precisely there is a positive constant C F such that

(3)

(Assumption (A))

Let ψ t (⋅ ) be a proper l.s.c. and convex function on V for all t ∈ [0, T]. We assume: (A1)If {t n } ⊂ [0, T] and t ∈ [0, T] with t n → t as n → ∞, then in the sense of Mosco [12] as n → ∞.

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