Integration by parts formulas for higher order operators and applications to boundary value problems

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] 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 coeffcients acting on vector valued functions. This class of operators contains the Lame operator of elasticity is discussed. In addition, as applications of our Green formulas, we 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.