I am facing problem to understand the notion of weak solution defined in page 3 of the article attached below: https://math.aalto.fi/~jkkinnun/papers/kuusi.pdf
My first question is:
1) On page 3 can you explain why the equation (2.2) acme? 2) In Lemma 3.1 why the test function $\eta=u^{2(1-p)}\phi$ is admissible?
Thank you very much.