Zobrazeno 1 - 10
of 16
pro vyhledávání: '"Max Engelstein"'
Publikováno v:
Forum of Mathematics, Sigma, Vol 11 (2023)
We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type functional whose free boundaries contain branch points in the strict
Externí odkaz:
https://doaj.org/article/cb42a06368a84c3582a8f50f7e31d900
Publikováno v:
Mathematische Zeitschrift. 299:2131-2169
In [David-Toro 15] and [David-Engelstein-Toro 19], (some of) the authors studied almost minimizers for functionals of the type first studied by Alt and Caffarelli in [Alt-Caffarelli 81] and Alt, Caffarelli and Friedman in [Alt-Caffarelli-Friedman 84]
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::007ac03f937935f01eab12f881008f4e
https://doi.org/10.1007/s00209-021-02719-5
https://doi.org/10.1007/s00209-021-02719-5
Publikováno v:
Revista Matemática Iberoamericana. 36:1375-1408
In non-variational two-phase free boundary problems for harmonic measure, we examine how the relationship between the interior and exterior harmonic measures of a domain Ω⊂Rn influences the geometry of its boundary. This type of free boundary prob
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::60145f5768e2729d768b1a30a04512f1
https://doi.org/10.4171/rmi/1170
https://doi.org/10.4171/rmi/1170
We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt- Caffarelli-Friedman type functional whose free boundaries contain branch points in the strict in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ff52fc7cad095b512bd960895a42eab5
We study the Riemannian quantiative isoperimetric inequality. We show that direct analogue of the Euclidean quantitative isoperimetric inequality is--in general--false on a closed Riemannian manifold. In spite of this, we show that the inequality is
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c81254d47848c5ed68d235812377bab
https://doi.org/10.52843/cassyni.1c2ykw
https://doi.org/10.52843/cassyni.1c2ykw
On any closed Riemannian manifold of dimension $n\geq 3$, we prove that if a function nearly minimizes the Yamabe energy, then the corresponding conformal metric is close, in a quantitative sense, to a minimizing Yamabe metric in the conformal class.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5c7bf521f3f25034878a94601da269e6
Publikováno v:
Duke Math. J. 169, no. 8 (2020), 1541-1601
In this paper we prove uniqueness of blow-ups and $C^{1,\log}$-regularity for the free-boundary of minimizers of the Alt-Caffarelli functional at points where one blow-up has an isolated singularity. We do this by establishing a (log-)epiperimetric i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b7299916ce77eb0ccb9504838fe2068
http://hdl.handle.net/11568/1060864
http://hdl.handle.net/11568/1060864
Autor:
Max Engelstein, Nick Edelen
Publikováno v:
Transactions of the American Mathematical Society. 371:2043-2072
In this paper we prove the rectifiability of and measure bounds on the singular set of the free boundary for minimizers of a functional first considered by Alt-Caffarelli. Our main tools are the Quantitative Stratification and Rectifiable-Reifenberg
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2ea3c845c45532b2288c95c8c9a07262
https://doi.org/10.1090/tran/7401
https://doi.org/10.1090/tran/7401
Autor:
Max Engelstein
Publikováno v:
Advances in Mathematics. 314:835-947
We study parabolic chord arc domains, introduced by Hofmann, Lewis and Nystr\"om, and prove a free boundary regularity result below the continuous threshold. More precisely, we show that a Reifenberg flat, parabolic chord arc domain whose Poisson ker
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::98fae96e336bd2fe9f932c534ab509ef
https://doi.org/10.1016/j.aim.2017.04.032
https://doi.org/10.1016/j.aim.2017.04.032
We provide a potential theoretic characterization of vanishing chord-arc domains under minimal assumptions. In particular we show that, if a domain has Ahlfors regular boundary, the oscillation of the logarithm of the interior and exterior Poisson ke
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6492d9059feeaccc83ebf69c72248333
http://arxiv.org/abs/1908.03033
http://arxiv.org/abs/1908.03033