A new proof of a regularity theorem for elliptic systems

Author:
K. Uhlenbeck

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

MSC:
Primary 35J45

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

MathSciNet review:
0315282

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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**].

**[1]**Shmuel Agmon,*The 𝐿_{𝑝} approach to the Dirichlet problem. I. Regularity theorems*, Ann. Scuola Norm. Sup. Pisa (3)**13**(1959), 405–448. MR**0125306****[2]**A.-P. Calderón,*Lebesgue spaces of differentiable functions and distributions*, Proc. Sympos. Pure Math., Vol. IV, American Mathematical Society, Providence, R.I., 1961, pp. 33–49. MR**0143037****[3]**Charles B. Morrey Jr.,*Multiple integral problems in the calculus of variations and related topics*, Univ. of California Publ. Math. (N. S.)**1**(1943), 1–130. MR**0011537****[4]**Norman G. Meyers,*An 𝐿^{𝑝}e-estimate for the gradient of solutions of second order elliptic divergence equations*, Ann. Scuola Norm. Sup. Pisa (3)**17**(1963), 189–206. MR**0159110**

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

Article copyright:
© Copyright 1973
American Mathematical Society