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Tuesday, April 23, 2019

**Abstract:** We will illustrate how factorizations of singular, even-order partial differential operators yield an elementary approach to classical inequalities of Hardy-Rellich-type. More precisely, using this factorization method, we will derive a general inequality and demonstrate how particular choices of the parameters contained in this inequality yield well-known inequalities, such as the classical Hardy and Rellich inequalities, as special cases. Actually, other special cases yield additional and apparently less well-known inequalities. We will indicate that our method is quite flexible when it comes to a variety of generalized situations involving the inclusion of remainder terms and higher-order operators. If time permits, we might illustrate a very recent new and most elementary proof in the one-dimensional context. This talk will be accessible to students. This is based on joint work with Lance Littlejohn, Isaac Michael, and Michael Pang.