Strong solutions to a class of boundary value problems on a mixed Riemannian-Lorentzian metric

TL;DR

This paper demonstrates the existence of strong solutions for a class of boundary value problems involving a mixed Riemannian-Lorentzian metric, addressing elliptic-hyperbolic systems in extended projective space.

Contribution

It introduces a novel approach to solving boundary value problems on mixed Riemannian-Lorentzian manifolds, expanding the understanding of elliptic-hyperbolic systems.

Findings

Existence of strong solutions for the specified boundary value problems.

Application of the method to Guderley-Morawetz-Keldysh problems.

Analysis within extended projective space.

Abstract

A first-order elliptic-hyperbolic system in extended projective space is shown to possess strong solutions to a natural class of Guderley-Morawetz-Keldysh problems on a typical domain.