il prossimo incontro del ciclo dei “Seminari di Analisi junior” si terr\u00e0\u00a0luned\u00ec 10 marzo 2025<\/b>\u00a0alle\u00a0ore 15.00<\/b>, nella Sala Riunioni Primo Livello (SR1<\/b>). Di seguito titoli e abstract.<\/p>\n
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Speaker:\u00a0<\/b>Paolo Cosentino, Postdoc presso Universit\u00e0 degli Studi di Roma Tor Vergata<\/p>\n
Titolo:\u00a0<\/b>A Harnack type inequality for singular Liouville type equations<\/p>\n
Abstract:\u00a0<\/b>We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actually more delicate and results in a nontrivial variation of the regular case. Part of the arguments of Chen-Lin can be adapted to the singular case by means of an isoperimetric inequality for surfaces with conical singularities. The rest of the proof actually requires a different approach, due to the loss of translation invariance of the problem.<\/p>\n
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Speaker:\u00a0<\/b>Giuseppe La Scala, Studente di Dottorato presso Universit\u00e0 degli Studi di Napoli Federico II<\/p>\n
Titolo:\u00a0<\/b>Rotating wave solutions in pure capillary drop equations.<\/p>\n Abstract:\u00a0<\/b>In 1879, Lord Rayleigh studied how the surface of a liquid drop evolves when interacting with the external environment by capillarity; in particular, profiles close to the spherical shape were taken into account. In 2D, some of them are numerically observed to rotate all the time, others are observed to fracture into spray by S. Dyachenko in 2022. \n","protected":false},"author":1,"featured_media":-1,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"tags":[],"event_type":[],"event_type_2":[],"class_list":["post-5694","ajde_events","type-ajde_events","status-publish","has-post-thumbnail","hentry","event_location-sala-professori-al-i-livello-del-dipartimento-di-matematica-ed-applicazioni-renato-caccioppoli"],"_links":{"self":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/5694","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events"}],"about":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/types\/ajde_events"}],"author":[{"embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5694"}],"version-history":[{"count":1,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/5694\/revisions"}],"predecessor-version":[{"id":5695,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/5694\/revisions\/5695"}],"wp:attachment":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5694"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5694"},{"taxonomy":"event_type","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fevent_type&post=5694"},{"taxonomy":"event_type_2","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fevent_type_2&post=5694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nThe existence of rotating waves for both 2D and 3D liquid capillary drops will be the object of this talk. In details, water wave equations for capillary drops will be introduced and it will be shown how their Hamiltonian structure and their symmetries can be exploited to get rotating waves as critical points of a suitable functional through a bifurcation-theoretical approach.
\nThis talk is based on a joint work with Pietro Baldi and Domenico Angelo La Manna in the 3D case and on a single-authored work by myself in the 2D case, both to appear on ArXiv.<\/p>\n<\/div>\n