Given that the central bankers do not know exactly how weak the economy is (the jobs figures, although important, are only one piece of evidence), let alone what damage the credit crunch will wreak, it would be irresponsible of them to slash the Fed funds rate.
This is not exactly a weak opposition, but they reckon they can beat all comers.
It is obvious that the critical point of the functional I ( u ) is exactly the weak solution of problem (1.1).
Clearly, the solutions of the equation (I_{lambda}^{prime} u)=0) are exactly the weak solutions of the problem ((P_{lambda })).
There exists a positive number such that if then for every the Cauchy-Neumann problem (2.1)–(2.3) has exactly one weak solution in, that satisfies (2.9).
In particular, associated with the variational kernel W = | ξ | p, (1.2) is reduced to the p-Dirichlet integral I [ u ] = ∫ Ω | g + d u | p, and the minimizers of the p-Dirichlet integral are exactly the weak solutions to the p-harmonic equation d ∗ ( | g + d u | p − 2 ( g + d u ) ) = 0.
In the first part, by applying Theorem 2.1, we prove the existence of a local minimum for the functional Φ − λ Ψ, where Φ ( u ) and Ψ ( u ) are functionals given in (2.7) for all u ∈ X. Obviously, Φ and Ψ satisfy all regularity assumptions requested in Theorem 2.1, and the critical points in X of the functional Φ − λ Ψ are exactly the weak solutions of problem (P).
The reaction of the West has proved to be weak, exactly as he expected.
And the voice, not weak exactly, but lacking utterly the capacity to inspire awe - nothing of the tragedian in Swinton.
"He had the uncanny capacity to know exactly what your weak point is, know what will make you feel small, to make you cringe," a friend of his tells Isaacson.
