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• W1973200733 abstract "Abstract We consider the asymptotic profiles of the nonlinear parabolic flows ( e u ) t = Δ u + λ e u to show the geometric properties of minimal solutions of the following elliptic nonlinear eigenvalue problems known as the Gelfand problem: Δ φ + λ e φ = 0 , φ > 0 in Ω φ = 0 on Ω posed in a strictly convex domain Ω ⊂ R n . In this work, we show that there is a strictly increasing function f ( s ) such that f − 1 ( φ ( x ) ) is convex for 0 λ ⩽ λ ⁎ , i.e., we prove that level set of φ is convex. Moreover, we also present the boundary condition of φ which guarantees the f-convexity of solution φ." @default.
• W1973200733 created "2016-06-24" @default.
• W1973200733 creator A5041150244 @default.
• W1973200733 creator A5069167592 @default.
• W1973200733 date "2014-06-01" @default.
• W1973200733 modified "2023-09-29" @default.
• W1973200733 title "Geometric properties of the Gelfand problem through a parabolic approach" @default.
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• W1973200733 doi "https://doi.org/10.1016/j.jmaa.2014.01.037" @default.
• W1973200733 hasPublicationYear "2014" @default.
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