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Article Dans Une Revue International Mathematics Research Notices Année : 2022

A Liouville-Type Theorem for the Lane–Emden Equation in a Half-space

Résumé

Abstract We prove that the Dirichlet problem for the Lane–Emden equation in a half-space has no positive solution that is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution that is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities.

Dates et versions

hal-03868772 , version 1 (23-11-2022)

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Citer

Louis Dupaigne, Boyan Sirakov, Philippe Souplet. A Liouville-Type Theorem for the Lane–Emden Equation in a Half-space. International Mathematics Research Notices, 2022, 2022 (12), pp.9024-9043. ⟨10.1093/imrn/rnaa392⟩. ⟨hal-03868772⟩
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