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