Abstract
We give an example of a nondivergent elliptic system showing that the classical Cordes condition of the Hölder property for the gradient of solution of a nondivergent elliptic equation is exact if properly extended onto systems.
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References
H. O. Cordes, “über die erste Randvertaufgabe bei quasilinear Differentialgleichungen zweiter Ordnung in mehr als zwei Variablen,”Mat. Ann.,131, 287–312 (1956).
G. Talenti, “Sopra una classe di equazioni ellittiche a coefficienti misurabili,”Ann. Mat. Pura Appl.,69, 285–304 (1965).
M. V. Safonov, “Unimprovability of estimates of the Hölder constants for solutions of linear elliptic equations with measurable coefficients,”Mat. Sb.,132, No. 2, 275–288 (1987).
E. A. Kalita “Regularity of solutions of Cordes elliptic systems of arbitrary order,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 12–15 (1989).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 292–294, February, 1995.
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Kalita, E.A. Exactness of the cordes condition of the Hölder property for the gradient of nondivergent elliptic systems. Ukr Math J 47, 344–346 (1995). https://doi.org/10.1007/BF01056725
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DOI: https://doi.org/10.1007/BF01056725