Continuous dependence of eigenvalues on the domain
Ivo M. Babuska, Rudolf Výborný · Czechoslovak Mathematical Journal · 1965
Recently I. HONG [1], [2], [3] investigated the continuous dependence of eigenfunctions and eigevalues for the Laplace operator on the domain.We employ the variational method, which enables us to prove the continuous dependence of eigen values and eigenfunctions on the domain for selfadjoint elliptic operators of higher orders.We employ the following notation: G will be an open bounded set of the rdimensional Euclidean space £^, G the closure of G, G the boundary of G; D{G) the set of infinitely continuously differentiable functions with compact support in G, for the elements of D{G) small Greek letters will be used.The symbol D\ where i = = (ï'i, 12,..., /V) {is being nonnegative integers), will denote the weak derivative of order i ~ (fj, i2,..., Q