Refinement of asymptotic behavior of the eigenvalues for the linearized Liouville–Gel’fand problem
Copyright policy )Refinement of asymptotic behavior of the eigenvalues for the linearized Liouville–Gel’fand problem
We determine the second term of the asymptotic expansions for the first m eigenvalues and eigenfunctions of the linearized Liouville-Gel'fand problem associated to solutions which blow-up at m points. Our problem is the case with an inhomogeneous coefficient in two dimensional domain and we extend the previous studies for the problem with a homogeneous coefficient. We also discuss in detail the required regularity of the coefficient necessary to get the conclusion.
blow-up analysis, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, Asymptotic distributions of eigenvalues in context of PDEs, Asymptotic behavior of solutions to PDEs, FOS: Mathematics, 35P15 (Primary) 35B40 (Secondary), Liouville-Gel'fand problem, Green's function, Hamiltonian, Analysis of PDEs (math.AP)
blow-up analysis, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, Asymptotic distributions of eigenvalues in context of PDEs, Asymptotic behavior of solutions to PDEs, FOS: Mathematics, 35P15 (Primary) 35B40 (Secondary), Liouville-Gel'fand problem, Green's function, Hamiltonian, Analysis of PDEs (math.AP)
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