Some remarks on the optimization of eigenvalue problems involving the p-Laplacian

• Autorzy: Pielichowski W.
• Języki publikacji: EN

Abstrakty

EN

Given a bounded domain Ω ⊂ Rn, numbers p > 1, ∝ ≥ 0 and A ∈ /0, /Ω/], consider the optimization problem: find a subset D ⊂ Ω, of measure A, for which the first eigenvalue of the operator u → - div(/∇u/p-2 ∇u) + ∝ΧD/u/p-2u with the Dirichlet boundary condition is as small as possible. We show that the optimal configuration D is connected with the corresponding positive eigenfunction u in such a way that there exists a number t ≥ 0 for which D = { u ≤ t}. We also give a new proof of symmetry of optimal solutions in the case when Ω is Steiner symmetric and p = 2.

Słowa kluczowe

EN

p-Laplacian; first eigenvalue; Steiner symmetry

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2008
• Tom: Vol. 28, no. 4
• Strony: 561--566
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Pielichowski W.

• Cracow University of Technology, Institute of Mathematics, ul. Warszawska 24, 31-155 Cracow, Poland,

Bibliografia

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