Unique continuation through transversal characteristic hypersurfaces

TL;DR

This paper establishes a unique continuation theorem for an ill-posed characteristic problem using geometric assumptions, Carleman estimates, and H"ormander's pseudo-convexity conditions, extending previous models.

Contribution

It extends existing model results on unique continuation for characteristic problems by employing geometric assumptions and advanced analytical tools.

Findings

Proves unique continuation under geometric conditions.

Utilizes Carleman estimates and pseudo-convexity.

Generalizes previous model results.

Abstract

We prove a unique continuation result for an ill-posed characteristic problem. A model problem of this type occurs in A.D.~Ionescu \& S.~Klainerman article (Theorem 1.1 in \cite{MR2470908}) and we extend their model-result using only geometric assumptions. The main tools are Carleman estimates and H\"ormander's pseudo-convexity conditions.