Il prossimo incontro del ciclo dei “Seminari di Analisi junior” si terr\u00e0 luned\u00ec 17 febbraio 2025 alle ore 15.00, nella Sala Riunioni Primo Livello (SR1). Di seguito titoli e abstract.<\/p>\n
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Antonia Diana:\u00a0<\/b>Length\u2013penalized elastic flow of curves with partial free boundary<\/p>\n
Abstract:\u00a0<\/b>Geometric gradient flows for elastic energies play an important role in mathematics and in many applications.
\nIn this talk we consider a curve with boundary points free to move on a line in R^2, which evolves by the L^2-gradient flow of the elastic energy, that is a linear combination of the Willmore and the length functional.
\nFor such planar evolution problem we study the short and long–time existence.
\nOnce we establish the well-posedness in the case of Navier boundary conditions, employing the Solonnikov theory for linear parabolic systems in H\u00f6lder space, we show that there exists a unique flow in a maximal time interval [0,T) and it is unique in a purely geometric sense. Finally, using energy methods we prove that maximal time is actually T=+\u221e.<\/p>\n
<\/p>\n
Domenico Vuono:\u00a0<\/b>Second and third order estimates for solutions to $p$-Laplace equations.<\/p>\n Abstract:\u00a0<\/b>We consider solutions to<\/p>\n<\/div>\n \u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002$$ – \\Delta_{p} u = f(x) \\quad \\text{in } \\Omega\\, ,$$<\/p>\n<\/div>\n when $p$ approaches the semilinear limiting case $p=2$ and we get third order estimates. As a consequence we deduce improved regularity properties of the stress field. The results presented in this seminar are contained in a recent paper with D. Baratta and B. Sciunzi. Finally, I present a $L^\\infty$-estimate for the second derivative of the solution. This is a recent result in preparation with F. Iandoli.<\/p>\n<\/div>\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-5545","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\/5545","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=5545"}],"version-history":[{"count":2,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/5545\/revisions"}],"predecessor-version":[{"id":5547,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=\/wp\/v2\/ajde_events\/5545\/revisions\/5547"}],"wp:attachment":[{"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5545"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5545"},{"taxonomy":"event_type","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fevent_type&post=5545"},{"taxonomy":"event_type_2","embeddable":true,"href":"https:\/\/www.matematica.unina.it\/index.php?rest_route=%2Fwp%2Fv2%2Fevent_type_2&post=5545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}