On extending solutions to Dirichlet problems across the boundary as solutions (Q1078747)

Let P be a second order differential oerator defined on an open manifold \(\tilde M\) and noncharacteristic with respect to the boundary \(\partial M\) of a bounded submanifold M. Suppose P has a real principal symbol having fiber-simple characteristics. Let u be an extendible distribution such that Pu\(\in C^{\infty}(M)\) and \(u|_{\partial M}\in C^{\infty}(\partial M)\). It is shown that near gliding points u can be microlocally extended such that Pu remains smooth.