How can they be sure they got it right when the previous canonical knowledge (Schauder) turned out to be false?
In what way did Schauder's work turn out to be false? It simply doesn't apply to the situations discussed here.
It wasn't wrong. It was proved for uniform materials. This paper extends it to non-uniform materials, with an additional condition.
In what way did Schauder's work turn out to be false? It simply doesn't apply to the situations discussed here.