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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1970, Volume 8, Issue 5, Pages 625–634 (Mi mz7010)

Some estimates of solutions of degenerate $(k,0)$-elliptic equations

L. P. Kuptsov

Moscow Institute of Physics and Technology

Abstract: A class of nonlinear second-order equations of divergent form is distinguished, whose solutions have properties recalling the properties of solutions of ordinary elliptic equations. In the linear case these are equations of the form
$$\sum_{j=1}^k\lambda_j(x)A_j^2u+\sum_{j=1}^k\mu_j(x)A_ju+c(x)u+f(x)=0$$
where the $A_j=\sum_{\alpha=1}^na_j^\alpha(x)\frac\partial{\partial x^\alpha}$ ($1\le j\le k$) are linearly independent first-order differential operators whose Lie algebra is of rank $n$, $2\le k\le n$, $\lambda_j(x)\ge0$ are functions which can become zero or increase in a definite way. Harnack's inequality is proved for nonnegative solutions of these equations.

Full text: PDF file (624 kB)

English version:
Mathematical Notes, 1970, 8:5, 820–826

Bibliographic databases:

UDC: 517.9

Citation: L. P. Kuptsov, “Some estimates of solutions of degenerate $(k,0)$-elliptic equations”, Mat. Zametki, 8:5 (1970), 625–634; Math. Notes, 8:5 (1970), 820–826

Citation in format AMSBIB
\Bibitem{Kup70} \by L.~P.~Kuptsov \paper Some estimates of solutions of degenerate $(k,0)$-elliptic equations \jour Mat. Zametki \yr 1970 \vol 8 \issue 5 \pages 625--634 \mathnet{http://mi.mathnet.ru/mz7010} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=279427} \zmath{https://zbmath.org/?q=an:0216.37901} \transl \jour Math. Notes \yr 1970 \vol 8 \issue 5 \pages 820--826 \crossref{https://doi.org/10.1007/BF01146939}