A remark on the semi-classical measure from -ℎ²\over2Δ+𝑉 with a degenerate potential 𝑉

This note is motivated by Evans (2004) and Anantharaman (2004). We study the semiclassical measure arising from the operator P ( h ) = − h 2 2 Δ + V ( x ) P(h)=-{h^2\over 2}\Delta +V(x) when the potential V V has degenerate minimum points. We will use the technique of integration by parts and some identities of Evans to derive information on the support of the measure.