Alborova, M. S. A density theorem. (Russian) Zbl 1021.46025 Vladikavkaz. Mat. Zh. 3, No. 3, 3-7 (2001). The author studies the question whether the space of infinitely-differentiable functions is dense in a Sobolev anisotropic space.Let \(K\) be a compact set in \(\mathbb R^n\) and let \(\left(L_p^l\right)_K\) denote the set of functions in \(L_p^l(\mathbb R^n)\) with compact supports in \(K\). Assuming that \(K\) satisfies some additional geometrical properties, the author proves that \(C_0^{\infty}(K)\) is dense in \(\left(L_p^l\right)_K\). Reviewer: V.Grebenev (Novosibirsk) MSC: 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 46E15 Banach spaces of continuous, differentiable or analytic functions 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:embedding theorem; Sobolev anisotropic space PDFBibTeX XMLCite \textit{M. S. Alborova}, Vladikavkaz. Mat. Zh. 3, No. 3, 3--7 (2001; Zbl 1021.46025) Full Text: EuDML Link