66 citations · 691 across the 59 of their papers we have counts for
5 papers · 1 filter
A note on zero sets of fractional sobolev functions with negative power of integrability
Armin Schikorra
We extend a Poincaré-type inequality for functions with large zero-sets by Jiang and Lin to fractional Sobolev spaces. As a consequence, we obtain a Hausdorff dimension estimate on…
General Existence of Solutions to Dynamic Programming Principle
Qing Liu, Armin Schikorra
We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear parti…
Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces
Piotr Hajlasz, Armin Schikorra
We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not…
A Game-Tree approach to discrete infinity Laplacian with running costs
Qing Liu, Armin Schikorra
We give a self-contained and elementary proof for boundedness, existence, and uniqueness of solutions to dynamic programming principles (DPP) for biased tug-of-war games with runni…
Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups
Piotr Hajlasz, Armin Schikorra, Jeremy T. Tyson
We provide a sufficient condition for the nontriviality of the Lipschitz homotopy group of the Heisenberg group, , in terms of properties of the classical homotopy…