Symmetry results for functions yielding best constants in Sobolev-type inequalities

By B. Kawohl. 2000

72 citations recorded by the source corpus.

I report on symmetry results for functions which yield sharp constants in various Sobolev-type inequalities. One of these results relies on a surprising convexity property.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5d804495b71fe7edccf73f74de7b9b4de4c29e0d

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In Mechanics of Materials

1. M. Belloni

Citations in the corpus

• The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p → ∞ (2004, background): “Our proof does not need this assumption and follows [29] (Prop.”
• Simplicity of the principal eigenvalue for indefinite quasilinear problems (2007, background): “(1.3) For positive weight w ∈ L∞(Ω), in a bounded domain Ω, it has been shown by Kawohl [17] (for w ≡ 1), Nazarov [25] that the minimizers of (1.3) are unique up to a constant factor whenever 1 q ≤ p.”