I've been working on this for a bit, and I think I have an idea. However, I still need some help making the idea work.
According to the textbook (Fritz John, p17), if we choose satisfying , then we have the following "conservation law":
and therefore if we choose then
Now, if we choose and then this will satisfy the conservation law, giving us
If I can show that this implies
then it will follow that
and taking limits as will give us the desired result .
But the problem is, I don't know how to show that (1) implies (2). Any suggestions ?
Thanks again guys !