Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in \(\mathbb R^3\) (Q2496569)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in \(\mathbb R^3\) |
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Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in \(\mathbb R^3\) (English)
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11 July 2006
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Under some conditions on \(f(u)\), we show that for small, the only solutions to the following elliptic equation \(\Delta u \lambda u + f(u) = 0\) in \(\Omega u>0\) in \(\Omega\) and \(\partial /\partial v = 0\) on \(\partial \Omega\), is constant.
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critical Sobolev exponent, Neumann equation, nonlinear elliptic PDEs
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