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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
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].

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  • [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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