E-raamat: Linear Holomorphic Partial Differential Equations and Classical Potential Theory

Introduction:
Some motivating questions;
The Cauchy-Kovalevskaya theorem with estimates;
Remarks on the Cauchy-Kovalevskaya theorem;
Zerner's theorem;
The method of globalizing families;
Holmgren's uniqueness theorem;
The continuity method of F. John;
The Bony-Schapira theorem;
Applications of the Bony-Schapira theorem: Part I - Vekua hulls;
Applications of the Bony-Schapira theorem: Part II - Szego's theorem
revisited;
The reflection principle; The reflection principle (continued);
Cauchy problems and the Schwarz potential conjecture;
The Schwarz potential conjecture for spheres;
Potential theory on ellipsoids: Part I - The mean value property;
Potential theory on ellipsoids: Part II - There is no gravity in the cavity;

Potential theory on ellipsoids: Part III - The Dirichlet problem;
Singularities encountered by the analytic continuation of solutions to the
Dirichlet problem;
An introduction to J. Leray's principle on propagation of singularities
through $\mathbb{C}^n$;
Global propagation of singularities in $\mathbb{C}^n$;
Quadrature domains and Laplacian growth;
Other varieties of quadrature domains;
Bibliography;
Index.