Simplicity of the principal eigenvalue for indefinite quasilinear problems

By B. Kawohl, Marcello Lucia, S. Prashanth. Advances in Differential Equations, 2007

70 citations recorded by the source corpus.

Given any domain Ω ⊆ RN , w ∈ L1 (Ω) and a differentiable function A : RN → [0, ∞) which is p-homogeneous and strictly convex, we consider the minimization problem inf Ω A( inf Ωu)/w(x)|u|q 1,: u ∈ D0 (Ω), w(x)|u|q < ∞ If the infimum is achieved and q = p > 1, without additional regularity assumptions on Ω or the weight function w, we show that the minimizer is unique up to a constant factor. The same conclusion holds when A is allowed to depend on x ∈ Ω and satisfies natural growth assumptions. Some of our results also hold when q < p

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c6dc68773edd0d97b2b03deb1b1eb73488189f1

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Citations in the corpus

• Minimization of the first eigenvalue in problems involving the bi-laplacian (2008, background): “For a proof of the uniqueness of the normalized first eigenfunction we refer to [1], [11], [14].”
• Eigenvalues and minimizers for a non-standard growth non-local operator (2018, unknown): “[13] and Fernández Bonder et al.”