Hello,

One defines .

is defined on the maximal subregion .

Now let and .

How to prove, that the following implication isnottrue in general:

In a book about functional analysis I read the following lemma:

"Let . If the inequality holds for all and for all then is weakly differentiable in with ."

Here the problem is , so the lemma can not be used.

Do you have a counter example?

Kind regards,

Alexander