Ordinary Differential Equations and Applied Dynamics Commons^™

Gradient Estimates And The Fundamental Solution For Higher-Order Elliptic Systems With Lower-Order Terms, Michael J. Duffy Jr.

Graduate Theses and Dissertations

Here we generalize the higher-order divergence-form elliptic differential equations studied by Barton in [4] by the inclusion of certain lower-order terms. The methods used here compare to those used in [4], with the addition of further Sobolev-type estimates to handle included lower-order terms. In section 3 we derive a Caccioppoli inequality in which we bound the L2 norm of the mth order gradient, in terms of the L2 norm of the solution. In section 5 we adapt some of the ideas from [9] to derive Lp bounds on gradients of solutions as a substitute for a reverse Holder inequality. Finally …