DENSITY OF C0∞(Rn)$ IN W1,p(x)(Rn)
WITH ASSUMPTION DENSITY OF C1(Rn)
Yasin Kaya
Department of Mathematics
Faculty of Education-Dicle University
Diyarbak{\i}r, 21280, TURKEY
Abstract. In this paper, we present a sufficient condition for the density of C0∞(Rn)$ in W1,p(x)(Rn) with assumption that p(x) satisfying a condition such that C1(Rn) is dense in W1,p(x)(Rn). The origin of our work comes from a similar question of H\"{a}st\"{o} \cite{h5} under the density of continuous or Hölder continuous whether it is possible to deduce the density of smooth functions.
AMS Subject classification: 46E30, 46E35
Keywords and phrases: variable exponent Sobolev spaces, density of smooth functions, convolution


Download full article from here (pdf format).

DOI: 10.12732/ijam.v27i6.1

Volume: 27
Issue: 6
Year: 2014