Abstract
Elliptic systems of a divergent type with a natural energy spaceW mp ∩W 1q are considered. Under certain restrictions imposed on the modulus of ellipticity of the lower part of the system, the Hölder property of the generalized solutions to this system and the Liouville theorem are established.
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I. V. Skrypnik, “On quasilinear elliptic equations of the higher order with continuous generalized solutions,”Differents. Uravn.,14, No. 6, 1104–1119 (1978).
A. I. Koshelev and S. I. Chelkak,Regularity of Solutions of Quasilinear Elliptic Systems, Teubner, Leipzig (1985).
E. A. Kalita, “Regularity of solutions of the elliptic systems of an arbitrary order of the Cordes type,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 5, 12–15 (1989).
E. A. Kalita, “Liouville theorem for higher order elliptic systems of Cordes type,”Ukr. Mat. Zh.,43, No. 2, 199–205 (1991).
I. V. Skrypnik,Methods of Investigation of Nonlinear Elliptic Boundary-Value Problems [in Russian], Nauka, Moscow (1990).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 942–947, July, 1993.
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Kalita, E.A. On nonlinear higher order elliptic systems positive in the first derivatives. Ukr Math J 45, 1042–1048 (1993). https://doi.org/10.1007/BF01057451
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DOI: https://doi.org/10.1007/BF01057451