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I have read in a couple of places (e.g. An Introduction to PDEs by Renardy and Rogers, p.309) that the smoothness hypotheses on the domain in the a priori estimate of Agmon, Douglis, and Nirenberg for elliptic systems can be weakened, but I haven't found a resource that goes into any detail yet. Can anybody point me towards a reference?

Many thanks in advance.

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Hi.

I don't clearly know the detail in the book by Renardy and Rogers. But one good book to look at for regularity/ a priori estimates for elliptic systems and calculus of variations for vector-valued functions is:

M. GIAQUINTA, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton U. Press, Princeton, 1983.

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