A Density Problem for Sobolev Spaces on Planar Domains

作者：Koskela, Pekka^*; Zhang, Yi Ru-Ya

来源：Archive for Rational Mechanics and Analysis, 2016, 222(1): 1-14.

DOI：10.1007/s00205-016-0994-y

• APPROXIMATION

We prove that for a bounded, simply connected domain Omega subset of R-2, the Sobolev space W-1,W-infinity (Omega) is dense in W-1,W-p (Omega) for any 1 <= p< infinity. Moreover, we show that if Omega is Jordan, then C-infinity (R-2) is dense in W-1,W-p (Omega) for 1 <= p< infinity.

• 出版日期2016-10