Density of smooth functions in variable exponent Sobolev spaces

2014/06/20 by Kostopoulos, Thanasis, Yannakakis, Nikos
#46E30 #46E35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1406.5385

Abstract

We show that if p_-≥ 2, then a sufficient condition for the density of smooth functions with compact support, in the variable exponent Sobolev space W^1,p(⋅)(\mathbb Rⁿ), is that the Riesz potentials of compactly supported functions of L^p(⋅)(\mathbb Rⁿ), are also elements of L^p(⋅)(\mathbb Rⁿ). Using this result we then prove that the above density holds if (i) p_-≥ n or if (ii) 2≤ p_-< n and p₊

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