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Kneser estimates for the coefficients of elliptic equations. (English. Russian original) Zbl 0699.35053

Sov. Math., Dokl. 36, No. 1, 101-103 (1987); translation from Dokl. Akad. Nauk SSSR 295, 556-548 (1987).
The first author [Vestn. Mosk. Univ., Ser. XV 1983, No.3, 8-13 (1983; Zbl 0527.35008); English translation in Mosc. Univ. Comput. Math. Cybernetics 7 (1983)] considered the elliptic equation \[ (1)\quad (- 1)^ m\sum_{| \alpha | =| \beta | =m}D^{\alpha}a_{\alpha \beta}(x)D^{\beta}u+a(x)u=0 \] and gave Kneser type estimates for its coefficients. In this paper new exact Kneser type estimates are provided. Such estimates were not known before, even in the case \(n=1\).
Reviewer: J.H.Tian

MSC:

35J15 Second-order elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs

Citations:

Zbl 0527.35008
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