The Gibbons conjecture stating the one-dimensional symmetry of certain solutions of semilinear elliptic equations has been proved by several authors. We show how attractivity properties of minimal propagating terraces of one-dimensional parabolic problems can be used in a proof of a version of this result and related statements.
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- Elliptic equations
- Gibbons conjecture
- one-dimensional symmetry
- propagating terraces
- traveling fronts