The Lp-dissipativity of certain differential and integral operators

The first part of the paper is a survey of some of the results previously obtained by the authors concerning the Lp-dissipativity of scalar and matrix partial differential operators. In the second part we give new necessary and, separately, sufficient conditions for the Lp-dissipativity of the “complex oblique derivative” operator. In the case of real coefficients we provide a necessary and sufficient condition. We prove also the Lp-positivity for a certain class of integral operators. ©2019 American Mathematical Society.