Caractérisation des ensembles essentiels

Abstract

In this work we study the essential sets for some Kato measure in $(R^d-\{0\left\}\right),$$d\ge 2$. Using the caracterisation of Picard principle via the Green kernel associated to the Schrödinger operator $\Delta -\mu$; we give a new caracterisation of such sets when $\mu =\left(f\right(.)/||.||{)}^2\lambda$ where $f$ is assumed to be rotation free nonnegative, decreasing and locally Hölder continuous on . In particular we obtain results given by T. Tada in the case where $d=2$ and $f\left(r\right)=-\log r$.