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

Yu, Yifeng

doi:10.1090/S0002-9939-06-08702-8

A remark on the semi-classical measure from ${-{h^2\over 2}\Delta +V}$ with a degenerate potential

Author: Yifeng Yu
Journal: Proc. Amer. Math. Soc. 135 (2007), 1449-1454
MSC (2000): Primary 35P20
DOI: https://doi.org/10.1090/S0002-9939-06-08702-8
Published electronically: November 13, 2006
MathSciNet review: 2276654
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Abstract: This note is motivated by Evans (2004) and Anantharaman (2004). We study the semiclassical measure arising from the operator $P(h)=-{h^2\over 2}\Delta +V(x)$ when the potential 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.

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