We consider general symmetric systems of first order linear partial differential operators on domains $\Omega \subset \mathbb R^d$ , and we seek sufficient conditions on the coefficients which ensure essential self-adjointness. The coefficients of the first order terms are only required to belong to $C^1 (\Omega)$ and there is no ellipticity condition. Our criterion writes as the completeness of an associated Riemannian structure which encodes the propagation velocities of the system. As an application we obtain sufficient conditions for confinement of energy for certain wave propagation problems of classical physics.

中文翻译：

---

关于$ \ mathbb R ^ d $中域上一阶微分算子的基本自伴性

我们考虑域$ \ Omega \ subset \ mathbb R ^ d $上的一阶线性偏微分算子的一般对称系统，并且我们在确保基本自伴随性的系数上寻求了充分条件。一阶项的系数只需要属于$ C ^ 1（\ Omega）$，并且没有椭圆率条件。我们的标准写为关联的黎曼结构的完整性，该结构编码系统的传播速度。作为一种应用，我们为经典物理学的某些波传播问题获得了限制能量的充分条件。