A density theorem.(Russian)Zbl 1021.46025

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 $$\left(L_p^l\right)_K$$.

MSC:

 4.6e+36 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 4.6e+16 Banach spaces of continuous, differentiable or analytic functions 4.6e+31 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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