Characterization of the traces on the boundary of functions in magnetic Sobolev spaces

Nguyen, Hoai-Minh;Van Schaftingen, Jean
(2020) Advances in mathematics — Vol. 371, p. 107246 (2020)

Files

190501188.pdf
  • Open Access
  • Adobe PDF
  • 353.28 KB
Download

Details

Authors
Abstract
We characterize the trace of magnetic Sobolev spaces defined in a half-space or in a smooth bounded domain in which the magnetic field A is differentiable and its exterior derivative corresponding to the magnetic field dA is bounded. In particular, we prove that, for d≥1 and p>1, the trace of the magnetic Sobolev space W1,pA(Rd+1+) is exactly W1−1/p,pA∥(Rd) where A∥(x)=(A1,…,Ad)(x,0) for x∈Rd with the convention A=(A1,…,Ad+1) when A∈C1(Rd+1+,Rd+1). We also characterize fractional magnetic Sobolev spaces as interpolation spaces and give extension theorems from a half-space to the entire space.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Nguyen, H.-M., & Van Schaftingen, J. (2020). Characterization of the traces on the boundary of functions in magnetic Sobolev spaces. Advances in mathematics, 371, 107246. https://doi.org/10.1016/j.aim.2020.107246 (Original work published 2020)