On the smoothness of the solution of the Dirichlet problem for hyperbolic systems in domains with conic or corner points
A Dirichlet problem for the hyperbolic system \[ \sum^n_{|p|,|q|=1} D^pa_{pq}(x, t) D^qu+ \sum^m_{|p|=1} a_p(x, t) D^pu+ a(x,t) u- u_{tt}= f\quad \text{in }\Omega, \] \[ u= u_t= 0\quad\text{for }t=0,\quad D^j_\nu u= 0\quad\text{for }x\in\partial\Omega,\quad j= 0,1,\dots, m-1, \] is considered in a bounded domain \(\Omega\subset \mathbb{R}^n\) with conic or angular points. Here \(a_{pq}\), \(a_p\) and \(a\) are \(s\times s\) infinitely differentiable matrices, \(D^j_\nu= {\partial^j\over\partial\nu^j}\), \(\nu\) is the outside normale of \(\partial\Omega\). The smoothness theorem is established for the generalized solution of this problem.
scientific article; zbMATH DE number 1557470