ANDREA KUBIN

Dottore di ricerca

ciclo: XXXIV

supervisore: E. Spadaro
relatore: E. Spadaro - M. Ponsiglione

Titolo della tesi: A variational approach to nonlocal interactions: discrete-to-continuum analysis, ground states and geometric evolutions

This thesis deals with variational models for systems governed by nonlocal interactions. In particular, we analyze systems of hard spheres governed by attractive Riesz potentials, surface energies related to fractional perimeters and gradient flows of such energies leading to local and nonlocal geometric evolutions; eventually, we consider similar problems for densities governed by Gagliardo-type seminorms, focussing on fractional heat flows.

Produzione scientifica

11573/1769278 - 2025 - A notion of s-fractional mass for 1-currents in higher codimension

Cicalese, M.; Heilmann, T.; Kubin, A.; Onoue, F.; Ponsiglione, M. - 01a Articolo in rivista

rivista: MATHEMATISCHE ANNALEN (Springer Verlag Germany:Tiergartenstrasse 17, D 69121 Heidelberg Germany:011 49 6221 3450, EMAIL: g.braun@springer.de, INTERNET: http://www.springer.de, Fax: 011 49 6221 345229) pp. 2157-2186 - issn: 0025-5831 - wos: WOS:001574643000001 (0) - scopus: 2-s2.0-105016746936 (0)

11573/1702034 - 2023 - The variational approach to s-fractional heat flows and the limit cases s → 0+ and s → 1−

Crismale, V.; De Luca, L.; Kubin, A.; Ninno, A.; Ponsiglione, M. - 01a Articolo in rivista

rivista: JOURNAL OF FUNCTIONAL ANALYSIS (New York: Academic Press.) pp. - - issn: 0022-1236 - wos: WOS:000934263400001 (19) - scopus: 2-s2.0-85147427539 (18)

11573/1665043 - 2022 - Failure of crystallization for generalized Lennard–Jones potentials and coarse graining to a rotating stars problem in one dimension

Crismale, Vito; Kubin, Andrea; Ninno, Angelo; Ponsiglione, Marcello - 01a Articolo in rivista

rivista: NONLINEAR ANALYSIS (Oxford, United Kingdom: Elsevier Science Limited) pp. - - issn: 0362-546X - wos: WOS:001041335400001 (1) - scopus: 2-s2.0-85133685323 (2)

11573/1612348 - 2022 - The core-radius approach to supercritical fractional perimeters, curvatures and geometric flows

De Luca, L.; Kubin, A.; Ponsiglione, M. - 01a Articolo in rivista

rivista: NONLINEAR ANALYSIS (Oxford, United Kingdom: Elsevier Science Limited) pp. 112585- - issn: 0362-546X - wos: WOS:000706958500022 (10) - scopus: 2-s2.0-85116410078 (10)

11573/1442398 - 2021 - Attractive Riesz potentials acting on hard spheres

Kubin, Andrea; Ponsiglione, Marcello - 01a Articolo in rivista

rivista: NONLINEARITY (IOP Publishing Limited:Dirac House, Temple Back, Bristol BS1 6BE United Kingdom:011 44 117 9297481, EMAIL: custserv@iop.org, INTERNET: http://www.iop.org, Fax: 011 44 117 9294318) pp. - - issn: 0951-7715 - wos: WOS:000612009600001 (5) - scopus: 2-s2.0-85100955785 (4)