Memoirs of the American Mathematical Society 2012; 77 pp; softcover Volume: 217 ISBN10: 0821853120 ISBN13: 9780821853122 List Price: US$60 Individual Members: US$36 Institutional Members: US$48 Order Code: MEMO/217/1019
 This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given. Table of Contents  Introduction
 Preliminaries
 Basic Solutions
 Example
 Asymptotic behavior of the basic solutions of \(\mathcal{L}\)
 The kernels
 The homogeneous equation \(\mathcal{L}u = 0\)
 The nonhomogeneous equation \(\mathcal{L}u = F\)
 The semilinear equation
 The second order equation: Reduction
 The homogeneous equation \(Pu = 0\)
 The nonhomogeneous equation \(Pu = F\)
 Normalization of a class of second order equations with a singularity
 Bibliography
