Solvability problem for nondiagonal elliptic systems with a quadratic nonlinearity in the gradient (The two-dimensional case)
β Scribed by A. Arkhipova
- Publisher
- Springer US
- Year
- 2005
- Tongue
- English
- Weight
- 174 KB
- Volume
- 127
- Category
- Article
- ISSN
- 1573-8795
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π SIMILAR VOLUMES
We prove the existence of bounded solutions for a class of nonlinear elliptic problems whose model is in the form: -div(a(x; u; Du)) = k1(|u|)|Du| p + k2(|u|)f; u β W 1;p 0 ( ) β© L β ( ); (\*) where a(x; Γ; ) ΒΏ b(|Γ|)| | p , b is a continuous monotone decreasing function and k1 and k2 are continuous
such problems goes back to B. RIEMANN in 1851. So A. I. GUSEINOV [251, V. K. NATALEVIC [39], [40], B. I. GEKHT [24] and others (cf. the recent monograph [26] of GUSEINOV and MUKHTAROV) applied iteration methods to these problems, whereas IT, POGORZELSKI in his monograph [C2], Chap. 19, 8 5 and other