Eigenvalue Asymptotics for Weighted Polyharmonic Operator with a Singular Measure in the Critical Case
Grigori V. Rozenblum, Eugene Shargorodsky · Functional Analysis and Its Applications · 2021
We find that, in the critical case $$2l= {\mathbf N} $$ , the eigenvalues of the problem $$\lambda(-\Delta)^{l}u=Pu$$ with the singular measure $$P$$ supported on a compact Lipschitz surface of an arbitrary dimension in $$ {\mathbb R} ^{ {\mathbf N} }$$ satisfy an asymptotic formula of the same order as in the case of an absolutely continuous measure.