Jeongsu Kyeong, Syracuse University
Abstract: The Neumann problem for second-order linear strongly elliptic differential operators in a Hilbert space setting offers a transparent view of coerciveness, where Garding's inequality applies, and the combination of coerciveness with the Lax-Milgram theorem ensures well-posedness. In contrast, there is no general existence theorem for solutions to the Neumann problem for higher-order elliptic operators. In this talk, I will describe coercive estimates for variational Neumann problems associated with higher-order constant coefficient elliptic operators.
This is an ongoing work with Gregory Verchota (Syracuse University).