Wave-type equations of low regularity

TL;DR

This paper establishes local existence and uniqueness results for a broad class of tensorial second order linear hyperbolic PDEs with low regularity coefficients using generalized functions.

Contribution

It introduces a framework for solving hyperbolic PDEs with low regularity coefficients, extending classical results to more general settings.

Findings

Proves local existence of solutions.

Establishes uniqueness of solutions.

Handles coefficients with low regularity.

Abstract

We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.