Operators of the form $Lu=\nabla\cdot (A\nabla u)$, that is, second order linear differential operators in divergence form, are by now very well understood. Two important generalizations are higher order operators $Lu=\nabla^m\cdot (A\nabla^m u)$, for $m\geq 2$ an integer, and operators with lower order terms $Lu=\nabla\cdot (A\nabla u) + \nabla\cdot (Bu) + C\cdot \nabla u+Du.$ In this talk we discuss our attempt to combine the two generalizations and study higher order operators with lower order terms.
Higher order elliptic differential equations with lower order terms
Ariel Barton, University of ArkansasAuthors: Ariel Barton and Michael Duffy Jr
2022 AWM Research Symposium
Analysis of Partial Differential Equations in Memory of David R. Adams