A new proof of a regularity theorem for elliptic systems

Uhlenbeck, K.

doi:10.1090/S0002-9939-1973-0315282-8

A new proof of a regularity theorem for elliptic systems
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by K. Uhlenbeck

Proc. Amer. Math. Soc. 37 (1973), 315-316

DOI: https://doi.org/10.1090/S0002-9939-1973-0315282-8

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Abstract:

We give a proof, which makes use of the Riesz-Thorin theorem, for a smoothness theorem for solutions of elliptic systems in divergence form with bounded measurable coefficients. The results imply an important theorem in two dimensions due to Morrey [3]. Meyers has used a similar technique to get these results for elliptic equations [4].

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Charles B. Morrey Jr., Multiple integral problems in the calculus of variations and related topics, Univ. California Publ. Math. (N.S.) 1 (1943), 1–130. MR 11537
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