Analysis of Heat Equations on Domains

This is the first comprehensive reference published on heat equations associated with non-self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats L[superscript p] properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory, and mathematical physics.' The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second-order elliptic operators in divergence form, heat kernel bounds, and their applications. It will also be of value to mathematical physicists.