The Analysis of Solutions of Elliptic Equations

This volume focuses on the analysis of solutions to general elliptic equations. A range of topics are touched upon, such as removable singularities, Laurent expansions, approximation by solutions, Carleman formulas and quasicon formality. While the basic setting is the Dirichlet problem for the Laplacian, there is some discussion of the Cauchy problem. Care is taken to distinguish between results which hold under more restrictive assumptions on the differential operators (homogeneous, of first order). Some parallels to the theory of functions of several complex variables are also sketched. The book should be of use to postgraduate students and researchers whose work involves partial differential equations, approximations and expansion, several complex variables and analytic spaces, potential theory and functional analysis. It could be used as a text for seminars and courses, as well as for independent study.