Tuesday, 24 February 2009

fa.functional analysis - Gradient of the energy functional in H1,2-norm

I have to use estimates for the gradient of the energy functional on the free loop space of a fixed compact manifold Q. As such, one considers H1,2-maps of the circle into Q. The energy functional is given by
mathcalE:H1,2(S1,Q)rightarrowIR,quadgammamapstofrac12int10|dotgamma(t)|2dt. Is there a neat formula for the gradient w.r.t. the H1,2 inner product?

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