论文信息 - A density property for fractional weighted Sobolev spaces

A density property for fractional weighted Sobolev spaces

In this paper we show a density property for fractional weighted Sobolev spaces. That is, we prove that any function in a fractional weighted Sobolev space can be approximated by a smooth function with compact support. The additional difficulty in this nonlocal setting is caused by the fact that the weights are not necessarily translation invariant.

E. Valdinoci | S. Dipierro

[1] Alexander Linke,et al. Optimal L2 velocity error estimate for a modified pressure-robust Crouzeix–Raviart Stokes element , 2015 .

[2] S. Dipierro,et al. Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential , 2015, 1506.07317.

[3] E. Valdinoci,et al. Bifurcation results for a fractional elliptic equation with critical exponent in R^n , 2014, 1410.3076.

[4] Jonas M. Tolle. Uniqueness of weighted Sobolev spaces with weakly differentiable weights , 2011, 1110.2888.

[5] E. Valdinoci,et al. Hitchhiker's guide to the fractional Sobolev spaces , 2011, 1104.4345.

[6] Vladimir I. Bogachev,et al. Differentiable measures and the Malliavin calculus , 2010 .

[7] E. Lieb,et al. Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators , 2007 .

[8] G. Folland. Real Analysis: Modern Techniques and Their Applications , 1984 .

[9] J. Cooper. SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONS , 1973 .

[10] Enrico Valdinoci,et al. DENSITY PROPERTIES FOR FRACTIONAL SOBOLEV SPACES , 2015 .

[11] T. Kilpeläinen,et al. Weighted Sobolev spaces and capacity. , 1994 .

[12] Valeria Chiadò Piat,et al. Some remarks about the density of smooth functions in weighted Sobolev spaces , 1994 .