This article is cited in 2 papers

Partial applicability of Moser's method to nonlinear elliptic systems

E. A. Kalita

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

Abstract: We consider nonlinear elliptic systems of divergent-type second-order partial differential equations with solutions $u\in W_p^1$. It is proved that $Du\in L_q$ with some $q\in(p;+\infty)$ and it is explicitly shown how $q$ depends on the ellipticity modulus of the system. Some conditions on the ellipticity modulus are obtained under which the solutions satisfy the Hölder conditions and the Liouville theorem holds.

Received: 27.02.1992

 English version: Mathematical Notes, 1995, 58:4, 1057–1065

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