Extremal Values of Half-Eigenvalues for p-Laplacian with Weights in L1 Balls. (2nd November 2010)

• Record Type: Journal Article
• Authors: Yan Yan, Ping Ping
• Other Names: Shakhmurov Shakhmurov V. V. Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-11-02
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/690342
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : For one-dimensional p -Laplacian with weights in ℒ γ : = L γ ( [ 0, 1 ], ℝ ) ( 1 ≤ γ ≤ ∞ ) balls, we are interested in the extremal values of the m th positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values are given by some best Sobolev constants.