Variational Boundary-Value Problems, Monotone Operators, and Variational Inequalities

Abstract

If K(u) is a differentiate functional on a Banach space u, and if P: U → U’ is its gradient, we have shown that the abstract problem of finding u ∈ U such that

$$\left\langle {p\left( u \right),n} \right\rangle _u = 0 \forall \eta \in u $$

((6.1))

is equivalent to finding critical points of K(u).