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Zapiski Nauchnykh Seminarov POMI, 2004, Volume 310, Pages 19–48
(Mi znsl804)
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This article is cited in 1 scientific paper (total in 1 paper)
New a priori estimates for $q$-nonlinear elliptic systems with strong nonlinearities in the gradient, $1<q<2$
A. A. Arkhipova Saint-Petersburg State University
Abstract:
We consider $q$-nonlinear nondiagonal elliptic systems, $1<q<2$, with strong nonlinear terms in the gradient. Under a smallness condition on the gradient of a solution in the Morry space $L^{q,n-q}$, we estimate $L^p$-norm of the gradient, $p>q$, and the Hölder norm of the solution for the case $n=2$. An abstract theorem on “quasireverse Hölder inequalities” proved by the author earlier is essencially used.
Received: 10.02.2004
Citation:
A. A. Arkhipova, “New a priori estimates for $q$-nonlinear elliptic systems with strong nonlinearities in the gradient, $1<q<2$”, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Zap. Nauchn. Sem. POMI, 310, POMI, St. Petersburg, 2004, 19–48; J. Math. Sci. (N. Y.), 132:3 (2006), 255–273
Linking options:
https://www.mathnet.ru/eng/znsl804 https://www.mathnet.ru/eng/znsl/v310/p19
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Abstract page: | 203 | Full-text PDF : | 69 | References: | 32 |
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