Inverse Spectral Problems for Elliptic Operators and Fractal Drums

Let Ω be an arbitrary non-empty bounded (or, more generally, of finite volume) open set in R n ( n ⩾ 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq1.tif"/> . with boundary ∂Ω. We consider the following variational eigenvalue problem { − Δ u = λ u  in  Ω , u = 0  on  ∂ Ω . ( P ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003067498/6ba0c26b-f086-40cc-86ed-1693dc596221/content/eq2.tif"/>