 Lions–Magenes lemma

Lions–Magenes lemma is a result in the field of functional analysis, particularly in the context of Sobolev spaces and partial differential equations. It provides a crucial tool for establishing the regularity and control of solutions to elliptic and parabolic differential equations. The lemma is typically used to handle boundary value problems, allowing one to obtain estimates of solutions in various norms, which is essential for understanding the existence and uniqueness of solutions as well as their continuity and differentiability properties.