Uniqueness for elliptic operators on with unbounded coefficients
Giorgio Metafune, Diego Pallara, Patrick J. Rabier, Roland Schnaubelt · Forum Mathematicum · 2010
Let A denote a general second order differential operator in divergence form, with real coefficients satisfying only local boundedness conditions. Then, A can be viewed as an unbounded operator A p on with maximal domain D ( A p ). The main result of this paper is a criterion for the injectivity of A p when p ∈ (1, ∞). This criterion is next used to establish the denseness of in D ( A p ) or, undermore general conditions, in a smaller natural domain. When p = 2, this also yields a positive answer to a selfadjointness question raised by Kato in 1981.