This Monograph contains a collection of problems arising in partial differential equations investigated by means of complex analysis approached in elementary ways.

This book is a collection of some problems that arise in partial differential equations which are not solvable for any right-hand sides modulo finite dimensional subspaces. Among them are: elliptic systems on a bounded domain which degenerate at all or part of the boundary, the Cauchy problem for elliptic systems, overdetermined systems, and systems with degenerate principal symbols. All of these problems are investigated in an elementary way by means of complex analysis.