A Function Theoretic Method for Treating the Three Dimensional Elliptic Linear Partial Differential Equation Laplacian Squared plus a Real Valued Entire Function Times U Equals Zero.

摘要

A function theoretic method is developed for a linear, fourth order elliptic equation consisting of a biharmonic operator plus a term without derivatives. The coefficient of the term without derivatives depends on all three variables. It is shown that this operator generates all strong solutions of the equation. This type of equation occurs in elasticity theory. Indeed, the equations concerning the important problem of elastic shells with arbitrary holes falls into a category which contains this equation. It is not difficult to solve equations from this category using similar methods. (Author)