Integration by Parts Formula for Higher Order Operators and Application to Boundary Value Problems

Date: 
Thursday, April 28, 2016 - 2:00pm
Location: 
124A Strickland
Speaker: 
Kayla Essner (Advisor: Prof. Dorina Mitrea)

Green formulas for differential operators are important tools in the study of Partial Differential Equations. The first such formula, published in 1828, was obtained by George Green for the Laplacian in three dimensions. Our work is concerned with Green formulas for higher-order homogeneous differential operators with constant complex coefficients acting on vector valued functions. This class of operators contains the Lamé operator of elasticity which will be discussed. In addition, as applications of our Green formulas, we will also prove uniqueness results
for the Dirichlet and Neumann boundary value problems for higher-order homogeneous differential operators with constant complex coefficients acting on vector valued functions.