Zobrazeno 1 - 10
of 47
pro vyhledávání: '"Tapio Rajala"'
Publikováno v:
Proceedings of the American Mathematical Society.
We prove that a bi-Lipschitz image of a planar B V BV -extension domain is also a B V BV -extension domain, and that a bi-Lipschitz image of a planar W 1 , 1 W^{1,1} -extension domain is again a W 1 , 1 W^{1,1} -extension domain.
Autor:
Tapio Rajala, Miguel García-Bravo
We show that a bounded domain in a Euclidean space is a $W^{1,1}$-extension domain if and only if it is a strong $BV$-extension domain. In the planar case, bounded and strong $BV$-extension domains are shown to be exactly those $BV$-extension domains
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4f478b34e9e0e9d48f21afbb0da660f0
http://urn.fi/URN:NBN:fi:jyu-202208254341
http://urn.fi/URN:NBN:fi:jyu-202208254341
We provide examples of infinitesimally Hilbertian, rectifiable, Ahlfors regular metric measure spaces having pmGH-tangents that are not infinitesimally Hilbertian.
19 pages
19 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1ce02ca17b0a0cbb0b8056885fece401
http://arxiv.org/abs/2111.06777
http://arxiv.org/abs/2111.06777
Publikováno v:
SIAM Journal on Mathematical Analysis. 51:2359-2371
We give an example of an absolutely continuous measure $\mu$ on $\mathbb{R}^d$ for any $d \ge 1$ such that no minimizer of the 3-marginal harmonic repulsive cost with all marginals equal to $\mu$ i...
Autor:
Tapio Rajala, Walter A. Ortiz
We show the density of smooth Sobolev functions $W^{k,\infty}(\Omega)\cap C^\infty(\Omega)$ in the Orlicz-Sobolev spaces $L^{k,\Psi}(\Omega)$ for bounded simply connected planar domains $\Omega$ and doubling Young functions $\Psi$.
Comment: 11 p
Comment: 11 p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6729c62850774070dfa64090c610aabb
http://urn.fi/URN:NBN:fi:jyu-202105203031
http://urn.fi/URN:NBN:fi:jyu-202105203031
We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev $W^{1,p}$-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.
16 pag
16 pag
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::705fd760ab3c9e5d384ef67b6317c1dd
http://arxiv.org/abs/2006.14213
http://arxiv.org/abs/2006.14213
Publikováno v:
Calculus of Variations and Partial Differential Equations
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak $(1,1)$-Poincar\'{e} inequality. The two main results we obtain are a decomposition theorem into inde
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz func
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c4f8c0806449c2b90e20a92b3233e983
Autor:
Tapio Rajala
We show that any bounded domain in a doubling quasiconvex metric space can be approximated from inside and outside by uniform domains.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e5c8c2a5c97dae612d96bc602f0143ad
Publikováno v:
Ark. Mat. 58, no. 1 (2020), 133-159
We show that the inner distance inside a bounded planar domain is at most the one-dimensional Hausdorff measure of the boundary of the domain. We prove this sharp result by establishing an improved Painlev\'e length estimate for connected sets and by
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b0e0031972a681c2f279913bc8e8116