Sure. This is why it seems logical to me to constraint both trial and
test space by Laplace equation. Nevertheless I did not think it over a
much.
For what it's worth, it seems logical to me as well... I just don't know
how to impose the second constraint.
So, if anyone could give me a hint or point me to a demo that shows how
to constrain test functions, I'd be very happy.
You don't need to constrain the test functions. This is actually the
whole point of the Lagrange multiplier. You end up with an equation with
the unconstrained test function, but if you choose a constrained test
function, the Lagrange multiplier term vanishes.
--cjc
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