3 citations · 3 across the 8 of their papers we have counts for
10 papers
Extension properties of planar subsets supporting a weak -Poincaré inequality
Miguel García-Bravo, Tapio Rajala
We study Sobolev and -extension properties of planar subsets. In particular, we prove that fat Sierpiński carpets that support a weak -Poincaré inequality are -…
On infinity thick quasiconvexity and applications
Miguel García-Bravo, Toni Ikonen, Zheng Zhu
We investigate geometric properties of a metric measure space where every function in the Newton--Sobolev space has a Lipschitz representative. We prove that when…
Extensions and approximations of Banach-valued Sobolev functions
Miguel García-Bravo, Toni Ikonen, Zheng Zhu
In complete metric measure spaces equipped with a doubling measure and supporting a weak Poincaré inequality, we investigate when a given Banach-valued Sobolev function defined on…
A necessary condition for Sobolev extension domains in higher dimensions
Miguel García-Bravo, Tapio Rajala, Jyrki Takanen
We give a necessary condition for a domain to have a bounded extension operator from to for the range . The condition is given in ter…
Two-sided boundary points of Sobolev-extension domains on Euclidean spaces
Miguel García-Bravo, Tapio Rajala, Jyrki Takanen
We prove an estimate on the Hausdorff-dimension of the set of two-sided boundary points of general Sobolev-extension domains on Euclidean spaces. We also present examples showing l…
Bi-Lipschitz invariance of planar - and -extension domains
Miguel García-Bravo, Tapio Rajala, Zheng Zhu
We prove that a bi-Lipschitz image of a planar -extension domain is also a -extension domain, and that a bi-Lipschitz image of a planar -extension domain is again…
Strong -extension and -extension domains
Miguel García-Bravo, Tapio Rajala
We show that a bounded domain in a Euclidean space is a -extension domain if and only if it is a strong -extension domain. In the planar case, bounded and strong -…
Normal tilings of a Banach space and its ball
Robert Deville, Miguel García-Bravo
We show some new results about tilings in Banach spaces. A tiling of a Banach space is a covering by closed sets with non-empty interior so that they have pairwise disjoint int…
Extraction of critical points of smooth functions on Banach spaces
Miguel García-Bravo
Let be an infinite-dimensional separable Hilbert space. We show that for every function , every open set with $C_f:=\{x\in E:\,Df(x)\; \text{is no…
Smooth approximations without critical points of continuous mappings between Banach spaces, and diffeomorphic extractions of sets
Daniel Azagra, Tadeusz Dobrowolski, Miguel García-Bravo
Let , be separable Hilbert spaces, and assume that is infinite-dimensional. We show that for every continuous mapping and every continuous function $\varepsil…