e prove
existence part of the proposition
(
Existence and
uniqueness for stationary problem
).
According to the proposition
(
A priory estimates for
Galerkin solution 1
)-1 and
(
Weak compactness of bounded
set
) there is a sequence
such
that
Then by the proposition
(
Rellich-Kondrachov
compactness
theorem
),
According to the proposition
(
A priory estimates for
Galerkin solution
1
)-2
so
that
We cannot immediately pass to the limit in
because of the
term in
.
Hence we
write
and, assuming that
,
,
Since
,
we now get rid of the problem
term:
and pass to the
limit
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