In what way did Schauder's work turn out to be false? It simply doesn't apply to the situations discussed here.
There was this sentence in the article: "...he realized that nonuniformly elliptic PDEs that seem well behaved can have irregular solutions even when they satisfy the condition Schauder had identified"
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There was this sentence in the article: "...he realized that nonuniformly elliptic PDEs that seem well behaved can have irregular solutions even when they satisfy the condition Schauder had identified"