Displaying similar documents to “On a volume constrained variational problem in SBV 2 ( Ω ) : part I”

Spectrum of the weighted Laplace operator in unbounded domains

Alexey Filinovskiy (2011)

Mathematica Bohemica


We investigate the spectral properties of the differential operator - r s Δ , s 0 with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm u L 2 , s ( Ω ) 2 = Ω r - s | u | 2 d x , we study the structure of the spectrum with respect to the parameter s . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.