On the uniqueness problem for Dirichlet operators
In this paper the author deals with the uniqueness problem for the classical Dirichlet form on a weighted real \(L^2\)-space when the underlying space is finite dimensional. The paper establish a criterion of strong uniqueness for the Dirichlet operator under local assumptions on the logarithmic derivative generalizing preceding results. The problem is reduced to the essential selfadjointness of a degenerate Dirichlet operator whose coefficients vanish outside a ball. Then the essential selfadjointness is proved for the operator on the ball using a method of a-priori estimates which turns out to be applicable for the situations with degeneracy. Next the uniqueness problem is considered in \(L^1\).
scientific article; zbMATH DE number 1270894
scientific article