The Liouville property and a conjecture of De Giorgi. (Q2711847)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Liouville property and a conjecture of De Giorgi. |
scientific article |
Statements
26 April 2001
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semilinear parabolic equations
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entire solutions
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Liouville theorem.
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The Liouville property and a conjecture of De Giorgi. (English)
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The authors study bounded entire solutions of the equation \(\Delta u+u-u^3=0\) in \({\mathbb R}^d\) and prove that under certain monotonicity conditions these solutions must be constant on hyperplanes. The proof uses a Liouville theorem for harmonic functions associated with a nonuniformly elliptic divergence form operator.
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