Lower Bounds for Dirichlet Eigenvalues of Higher-order Elliptic Operators
Fu Ai · Mathematica Applicata · 2000
Let Ω be a bounded domain in R m(m≥2) with sufficiently smooth boundary. Under the Dirichlet boundary condition, the eigenvalue problem of elliptic operators (-1) p∑|α|=|β|=p α(A αβ β) with order 2p(p≥1) is discussed. This paper is to give a lower bound for the eigenvalue. Our bound depends on the volume of the domain Ω, except for the dimension m.