Zobrazeno 1 - 10
of 111
pro vyhledávání: '"Steve Hofmann"'
Publikováno v:
Dindos, M, Hofmann, S & Pipher, J 2023, ' Regularity and Neumann Problems for Operators with Real Coefficients Satisfying Carleson Conditions ', Journal of functional analysis, vol. 285, no. 6, 110024 . https://doi.org/10.1016/j.jfa.2023.110024
In this paper, we continue the study of a class of second order elliptic operators of the form $\mathcal L=\mbox{div}(A\nabla\cdot)$ in a domain above a Lipschitz graph in $\mathbb R^n,$ where the coefficients of the matrix $A$ satisfy a Carleson mea
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a99ccda0dfde870223afa2fc6ea0ae8f
http://arxiv.org/abs/2207.10366
http://arxiv.org/abs/2207.10366
Autor:
Steve Hofmann, Olli Tapiola
Publikováno v:
Annales de l'Institut Fourier. 70:1595-1638
Suppose that $E \subset \mathbb{R}^{n+1}$ is a uniformly rectifiable set of codimension $1$. We show that every harmonic function is $\varepsilon$-approximable in $L^p(\Omega)$ for every $p \in (1,\infty)$, where $\Omega := \mathbb{R}^{n+1} \setminus
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8a60d8657517da933155043fe8a90bf1
https://doi.org/10.5802/aif.3359
https://doi.org/10.5802/aif.3359
Publikováno v:
IAS/Park City Mathematics Series. :155-198
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e20585a3283c6be8d24993e2dc76791c
https://doi.org/10.1090/pcms/027/05
https://doi.org/10.1090/pcms/027/05
Publikováno v:
Digital.CSIC. Repositorio Institucional del CSIC
instname
instname
We generalize to the setting of 1-sided chord-arc domains, that is, to domains satisfying the interior Corkscrew and Harnack Chain conditions (these are respectively scale-invariant/quantitative versions of the openness and path-connectedness) and wh
Externí odkaz:
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https://doi.org/10.1090/tran/8148
https://doi.org/10.1090/tran/8148
Publikováno v:
International Mathematics Research Notices. 2021:18300-18366
We solve the Neumann problem, with nontangential estimates, for higher-order divergence form elliptic operators with variable $t$-independent coefficients. Our results are accompanied by nontangential estimates on higher-order layer potentials.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::78b7e58da2277afc904a7c9130a8a3fa
https://doi.org/10.1093/imrn/rnaa051
https://doi.org/10.1093/imrn/rnaa051
We prove that coronizations with respect to arbitrary d-regular sets (not necessarily graphs) imply big pieces squared of these (approximating) sets. This is known (and due to David and Semmes in the case of sufficiently large co-dimension, and to Az
Externí odkaz:
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http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-492118
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-492118
Autor:
Steve Hofmann, Alyssa Genschaw
Publikováno v:
The Journal of Geometric Analysis. 30:1530-1564
Following a result of Bennewitz–Lewis for non-doubling harmonic measure, we prove a criterion for non-doubling caloric measure to satisfy a weak reverse Holder inequality on an open set $$\Omega \subset \mathbb {R}^{n+1}$$, assuming as a background
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::db08a266ab7207178098f5be6a36652a
https://doi.org/10.1007/s12220-019-00212-4
https://doi.org/10.1007/s12220-019-00212-4
Autor:
Steve Hofmann
Publikováno v:
Acta Mathematica Sinica, English Series. 35:1011-1026
It is a well-known folklore result that quantitative, scale invariant absolute continuity (more precisely, the weak-A∞ property) of harmonic measure with respect to surface measure, on the bound¬ary of an open set Ω ⊂ ℝn+1 with Ahlfors-David
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4c3be40bd4728079e07070cc50362b4d
https://doi.org/10.1007/s10114-019-8444-z
https://doi.org/10.1007/s10114-019-8444-z
Publikováno v:
Proceedings of the London Mathematical Society. 119:613-653
In this paper we establish square-function estimates on the double and single layer potentials with rough inputs for divergence form elliptic operators, of arbitrary even order 2m, with variable t-independent coefficients in the upper half-space.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5a0ff93f52806e9f4d9364c41447b1f7
https://doi.org/10.1112/plms.12241
https://doi.org/10.1112/plms.12241
Autor:
Simon Bortz, Steve Hofmann
Publikováno v:
Potential Analysis. 53:329-355
We show that a suitable quantitative Fatou Theorem characterizes uniform rectifiability in the codimension 1 case.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6fc661fe4555aef05595fecdfbcabd98
https://doi.org/10.1007/s11118-019-09771-1
https://doi.org/10.1007/s11118-019-09771-1