ShowMe Analysis Meeting 2004 June 3-5, 2004 University of Missouri Columbia, Missouri

Igor Verbitsky (University of Missouri, Columbia)
Form boundedness and subordination for Schrödinger operators and vector fields

Abstract: We will present recent solutions to the relative form boundedness problem for operators and with real- or complex-valued distributional coefficients. Such results and associated integral inequalities in Sobolev norms are used extensively in quantum mechanics, dynamics, PDE, and Markov processes.

Related compactness and infinitesimal form boundedness criteria will be discussed, along with characterizations of Trudinger type conditions, L^p analogues, and applications to nonlinear elliptic equations.