Bartłomiej Dyda, Michał Kijaczko
Abstract
We prove that smooth $C^\infty$ functions are dense in fractional Sobolev spaces on an arbitrary open set. We also consider weighted fractional Sobolev spaces and give some sufficient conditions under which an analogous result holds.
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We prove that smooth $C^\infty$ functions are dense in fractional Sobolev spaces on an arbitrary open set. We also consider weighted fractional Sobolev spaces and give some sufficient conditions under which an analogous result holds.
Key concepts: Sobolev space, Mathematics, Open set, Type (biology), Pure mathematics, Set (abstract data type), Fractional calculus, Sobolev inequality