Ariel Barton, University of Arkansas
Authors: Ariel Barton and Michael Duffy Jr
2022 AWM Research Symposium
Analysis of Partial Differential Equations in Memory of David R. Adams

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.

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