Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Matteo Cozzi"'
Publikováno v:
Communications in Analysis and Geometry. 29:761-777
We prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. This result generalizes fractional versions of classical theorems due to Bernstein and Moser. Our arguments rely on a ge
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0e4e92939e36a32e9ed37d0961c1d882
https://doi.org/10.4310/cag.2021.v29.n4.a1
https://doi.org/10.4310/cag.2021.v29.n4.a1
Autor:
Nicola Abatangelo, Matteo Cozzi
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the non-existence regi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3226486e18d767f267d04e223daf385d
http://arxiv.org/abs/2005.09515
http://arxiv.org/abs/2005.09515
Autor:
Enrico Valdinoci, Matteo Cozzi
Publikováno v:
Cozzi, M & Valdinoci, E 2020, ' On the growth of nonlocal catenoids ', Rendiconti Lincei. Matematica e Applicazioni, vol. 31, no. 1, pp. 237-248 . https://doi.org/10.4171/RLM/888
As well known, classical catenoids in R 3 possess logarithmic growth at infinity. In this note we prove that the case of nonlocal minimal surfaces is significantly di¤erent, and indeed all nonlocal catenoids must grow at least linearly. More general
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a349465b39ec5e3fbe8af7b33c3b1d9a
https://purehost.bath.ac.uk/ws/files/190327488/nota_rigsublin_finale.pdf
https://purehost.bath.ac.uk/ws/files/190327488/nota_rigsublin_finale.pdf
Autor:
Matteo Cozzi, Luca Lombardini
We develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison principles, rearrangement inequalities, and the equivalence of several not
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c1d0598fd3b5b8cada21f0bb0724ae86
Autor:
Matteo Cozzi
Publikováno v:
Journal of Functional Analysis. 272:4762-4837
We study energy functionals obtained by adding a possibly discontinuous potential to an interaction term modeled upon a Gagliardo-type fractional seminorm. We prove that minimizers of such non-differentiable functionals are locally bounded, H\"older
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::32700c352e68629840fbc45990b0c2f1
https://doi.org/10.1016/j.jfa.2017.02.016
https://doi.org/10.1016/j.jfa.2017.02.016
Autor:
Matteo Cozzi, Enrico Valdinoci
Publikováno v:
Journal de l’École polytechnique — Mathématiques. 4:337-388
where K : Rn × Rn → [0,+∞] is a measurable kernel comparable to that of the fractional Laplacian of order 2s, with s ∈ (0, 1), and W : Rn × R→ [0,+∞) is a smooth double-well potential, with zeroes at u = ±1. Both K and W are assumed to b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b2d6847257ca90f9922fab1ef6f9821a
https://doi.org/10.5802/jep.45
https://doi.org/10.5802/jep.45
Autor:
Xavier Cabré, Matteo Cozzi
Publikováno v:
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname
Duke Math. J. 168, no. 5 (2019), 775-848
Universitat Politècnica de Catalunya (UPC)
Recercat. Dipósit de la Recerca de Catalunya
instname
Duke Math. J. 168, no. 5 (2019), 775-848
We consider the class of measurable functions defined in all of $\mathbb{R}^n$ that give rise to a nonlocal minimal graph over a ball of $\mathbb{R}^n$. We establish that the gradient of any such function is bounded in the interior of the ball by a p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd0f856326bddc84af3283b087a6f6cb
http://hdl.handle.net/2117/134057
http://hdl.handle.net/2117/134057
Autor:
Matteo Cozzi
Publikováno v:
Contemporary Research in Elliptic PDEs and Related Topics ISBN: 9783030189204
Cozzi, M 2019, Fractional De Giorgi classes and applications to nonlocal regularity theory . in Contemporary Research in Elliptic PDEs and Related Topics . Springer INdAM (SINDHAMS) Series, vol. 33, Springer International Publishing, Cham, Switzerland, pp. 277-299 . https://doi.org/10.1007/978-3-030-18921-1_7
Cozzi, M 2019, Fractional De Giorgi classes and applications to nonlocal regularity theory . in Contemporary Research in Elliptic PDEs and Related Topics . Springer INdAM (SINDHAMS) Series, vol. 33, Springer International Publishing, Cham, Switzerland, pp. 277-299 . https://doi.org/10.1007/978-3-030-18921-1_7
We present some recent results obtained by the author on the regularity of solutions to nonlocal variational problems. In particular, we review the notion of fractional De Giorgi class, explain its role in nonlocal regularity theory, and propose some
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7354e1255ebe4994d53a81fcb317015a
https://doi.org/10.1007/978-3-030-18921-1_7
https://doi.org/10.1007/978-3-030-18921-1_7
Autor:
Matteo Cozzi
Publikováno v:
Annali di Matematica Pura ed Applicata (1923 -). 196:555-578
We prove interior $H^{2s-\varepsilon}$ regularity for weak solutions of linear elliptic integro-differential equations close to the fractional $s$-Laplacian. The result is obtained via intermediate estimates in Nikol'skii spaces, which are in turn ca
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c3e314ef298b61742403ed3d66e7a321
https://doi.org/10.1007/s10231-016-0586-3
https://doi.org/10.1007/s10231-016-0586-3
Autor:
Tommaso Passalacqua, Matteo Cozzi
Publikováno v:
Journal of Differential Equations. 260:6638-6696
We are interested in the study of local and global minimizers for an energy functional of the type 1 4 ∬ R 2 N ∖ ( R N ∖ Ω ) 2 | u ( x ) − u ( y ) | 2 K ( x − y ) d x d y + ∫ Ω W ( u ( x ) ) d x , where W is a smooth, even double-well p
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d1709634180e05094751ea05cf1cf481
https://doi.org/10.1016/j.jde.2016.01.006
https://doi.org/10.1016/j.jde.2016.01.006