|LECTURE:||MWF 1500 - 1550||Kidder 280||CRN 26821|
|Instructor:||R.E. Showalter||Kidder email@example.com|
We develop the notions of weak derivatives, Sobolev spaces, boundary trace and weak formulations of elliptic boundary-value problems and of initial-boundary-value problems for parabolic or hyperbolic PDEs. These are resolved by variants of the closed-range theorem, variational methods, and the generation theory of semigroups of contractions. Extensions to nonlinear problems and systems will be presented (as Supplementry material) according to the interests of the class.
1. HSM Chapter 1: pp. 1 - 18.
2. HSM Chapter 2: pp. 31 - 35, generalized functions.