Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 235-253

DENSITY PROPERTIES FOR FRACTIONAL SOBOLEV SPACES

Alessio Fiscella, Raffaella Servadei and Enrico Valdinoci

Università di Milano, Dipartimento di Matematica
Via Cesare Saldini 50, 20133 Milano, Italy; alessio.fiscella 'at' unimi.it

Università della Calabria, Dipartimento di Matematica e Informatica
Ponte Pietro Bucci 31 B, 87036 Arcavacata di Rende (Cosenza), Italy; servadei 'at' mat.unical.it

Università di Milano, Dipartimento di Matematica
Via Cesare Saldini 50, 20133 Milano, Italy;
and Weierstrass-Institut für Angewandte Analysis und Stochastik
Mohrenstrasse 39, 10117 Berlin, Germany; enrico.valdinoci 'at' wias-berlin.de

Abstract. Aim of this paper is to give the details of the proof of some density properties of smooth and compactly supported functions in the fractional Sobolev spaces and suitable modifications of them, which have recently found application in variational problems. The arguments are rather technical, but, roughly speaking, they rely on a basic technique of convolution (which makes functions C^∞), joined with a cut-off (which makes their support compact), with some care needed in order not to exceed the original support.

2010 Mathematics Subject Classification: Primary 46E35, 35A15, 35S15; Secondary 47G20, 45G05.

Key words: Fractional Sobolev spaces, density properties, integrodifferential operators, fractional Laplacian.

Reference to this article: A. Fiscella, R. Servadei and E. Valdinoci: Density properties for fractional Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), 235-253.

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doi:10.5186/aasfm.2015.40xx