Displaying similar documents to “On the regularity of boundary traces for the wave equation”

Microlocal regularity at the boundary for pseudo-differential operators with the transmission property (I)

Maurice De Gosson (1982)

Annales de l'institut Fourier

Similarity:

This work is devoted to a systematic study of the microlocal regularity properties of pseudo-differential operators with the transmission property. We introduce a “boundary singular spectrum”, denoted ∂ W F ω ( u ) for distributions u ∈ D ' ( R + n ) , regular in the normal variable x n (thus, ∂ W F ω ( u ) = ∅ means that u ∈ ∩ s + t = 1 / 2 H s + t near the boundary), and it is shown that ∂ W F ω - m [ P ( u 0 ) x n > 0 ] is a subset of ∂ W F ( u ) if P has degree m and the transmission property. We finally prove that these results can bef used to examinate the (microlocal) regularity of the solutions...