Traces for the dual of Sobolev spaces. (Portuguese) Zbl 0769.46028

Milla Miranda, Manuel

Bol. Soc. Parana. Mat. (2) 11, No. 2, 131-157 (1990).

Let \(\Omega\) be an open bounded set with sufficiently regular boundary \(\Gamma\). In this paper the author constructs a trace map \[ \text{Tr}: H^{-k}(0,T;H^ m(\Omega))\to H^{-k} \left( 0,T; \prod_{j=0}^{m- 1} H^{m-j-1/2} (\Gamma)\right), \] and applies his result to the study of certain hyperbolic problems.

Reviewer: M.Milman (Boca Raton)

MSC:

46E35

Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Keywords:

dual of Sobolev spaces; trace map; hyperbolic problems