Extension of Solutions to Holomorphic Partial Differential Equations

TL;DR

This paper investigates conditions under which solutions to certain holomorphic PDEs exist locally but cannot be extended across boundary points of pseudoconvex domains, highlighting limitations in holomorphic extension.

Contribution

It provides new sufficient conditions for the existence of boundary solutions to holomorphic PDEs that are non-extendable across boundary points.

Findings

Identifies conditions for non-extendability of solutions at boundary points

Establishes existence criteria for solutions near boundary points

Highlights limitations in holomorphic extension for PDE solutions

Abstract

Given a strictly pseudoconvex domain G and a linear partial differential operator P with holomorphic coefficients, we derive sufficient conditions for the existence of a solution to Pu = 0 which is holomorphic in G near a point p in the boundary or G, but cannot be extended holomorphically across p.