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

(1)

If I can show that this implies

(2)

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 !