4 papers
Rectifiability of the straight visible boundary and the limits of segment-based Hardy criteria
H. Abbas, A. Azzouz
Weighted Hardy inequalities on a domain can be deduced from lower Hausdorff-content bounds on suitable visible parts of the boundary, and it is natural to look for v…
A nonlocal transmission problem on a hybrid continuous-discrete domain
Hafida Abbas, Abdelhalim Azzouz
We study a quadratic nonlocal variational problem on a hybrid domain formed by a compact interval and finitely many discrete points. The associated energy splits into continuous, d…
Fractional Sobolev Spaces and Variational Problems with Variable-Order Operators on Time Scales
Hafida Abbas, Abdelhalim Azzouz
We construct fractional Sobolev spaces on arbitrary time scales, both in one dimension and on product time scales. In 1D, we define throu…
Towards a Gagliardo-Type Theory of Fractional Sobolev Spaces on Arbitrary Time Scales
Hafida Abbas, Abdelhalim Azzouz, Praveen Agarwal +1
We propose a systematic Gagliardo-type formulation of fractional Sobolev spaces on arbitrary time scales, based on the Lebesgue Delta-measure and the off-diagonal interaction domai…