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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] S. Agmon, The $ {L_p}$ approach to the Dirichlet problem. I. Regularity theorems, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 405-448. MR 0125306 (23:A2609)
  • [2] A. P. Calderón, Lebesgue spaces of differentiable functions and distributions, Proc. Sympos. Pure Math., vol. 4, Amer. Math. Soc., Providence, R.I., 1961, pp. 33-49. MR 26 #603. MR 0143037 (26:603)
  • [3] C. B. Morrey, Jr., Multiple integrals problems in the calculus of variations and related topics, Univ. California Publ. Math. 1 (1943), 1-130. MR 6, 180. MR 0011537 (6:180b)
  • [4] N. G. Meyers, An $ {L^p}$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa (3) 17 (1963), 189-206. MR 28 #2328. MR 0159110 (28:2328)

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