Unique continuation through transversal characteristic hypersurfaces

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 Hörmander's pseudo-convexity conditions.

20 pages, 1 figure, to appear in the Journal d'Analyse Mathématique

References in corpus (1)

• Uniqueness results for ill posed characteristic problems in curved space-times

Cited by in corpus (2)

• Recovering initial values from light cone traces of solutions of the wave equation
• On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds