et
be the solution of the problem
(
Variational toy problem
) and
be the solution of the problem
(
Approximate toy problem
). We seek
conditions for the convergence
as
.
We introduce the
norm
By definition of
and the formula (
Holder inequality
) we
have
We
estimate
Let
.
Note that
and, by subtracting the problems
(
Variational toy problem
) and
(
Approximate toy problem
),
satisfy
.
Hence, we
continue
Thus,
or
for any
.
