On fractional Poincaré inequalities

By R. Hurri-Syrjänen, Antti V. Vahakangas. 2013

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Fractional p-Laplacian evolution equations (2016, methodology): “1) we use the following fractional Poincaré inequality (see [11], [22]): given 1 ≤ p <∞, there exists a constant C such that, ∫”
A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations (2015, background): “ith zero average (4.7) jv(x)jqdx 1 q C \B(x;˝(x)) jv(x) pv(y)jp jx yjn+˙p dydx ! 1 : The parameters ˝ and ˙can be taken arbitrarily as long as ˝;˙2(0;1), while 1 <pq np n ˙p , p<n=˙. In [29] the domain is assumed to belong to the class of John domains (for a denition and properties of this c”