Integration by Parts in Sobolev Spaces

This lecture covers the integration by parts formula in Sobolev spaces, the weak formulation of linear elliptic PDEs, and the Poincaré inequality in $W^{1,p}_0$. It explores the standard version of the integration by parts formula, the weak formulation of PDEs, and the extension of functions in Sobolev spaces. The instructor discusses the proof of the Poincaré inequality and its application in the context of sounded domains with C2 boundaries.