10 citations · 43 across the 42 of their papers we have counts for
5 papers · 1 filter
Coarse and pointwise tangent fields
Guy C. David, Sylvester Eriksson-Bique, Raanan Schul
Alberti, Csörnyei and Preiss introduced a notion of a "pointwise (weak) tangent field" for a subset of Euclidean space -- a field that contains almost every tangent line of every c…
Fragment-wise differentiable structures
David Bate, Sylvester Eriksson-Bique, Elefterios Soultanis
The -modulus of curves, test plans, upper gradients, charts, differentials, approximations in energy and density of directions are all concepts associated to the theory of Sobol…
Density of Lipschitz functions in Energy
Sylvester Eriksson-Bique
In this paper, we show that the density in energy of Lipschitz functions in a Sobolev space holds for all whenever the space is complete and sepa…
Self-improvement of weighted pointwise inequalities on open sets
Sylvester Eriksson-Bique, Juha Lehrbäck, Antti V. Vähäkangas
We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this pu…
Self-improvement of pointwise Hardy inequality
Sylvester Eriksson-Bique, Antti V. Vähäkangas
We prove the self-improvement of a pointwise -Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.