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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
6
votes
Applications of the Calderon-Zygmund theory to PDE's
starting with the laplacian is a good idea. I suggest Stein old book about Singular integrals.
Then, constant coefficient operators in principal part is just change of choordinates.
Then you could mov …
3
votes
General version of Weyl's lemma
unfortunately Weyl lemma cannot be generalized to any divergence form elliptic operator. The problem is given by the smoothness of the coefficients $a_{ij}$. There is a huge literature on the subject. …