Prof. Antonio Greco<\/strong> Abstract<\/strong><\/p>\n The course is an introduction to the problem of\u00a0determining the shape of solutions to boundary-value problems\u00a0for second-order partial differential equations, mainly\u00a0of elliptic type, occasionally parabolic.<\/p>\n Outline<\/strong><\/p>\n – Review of the weak maximum principle, the strong maximum principle, and the Hopf lemma. Schedule<\/strong><\/p>\n The course spans over 8 lectures of 2 hours each (16 hours total), one lecture per week. Details will be specified on the occasion of the first lecture, which will be given on October 20, 2023 at 4 p.m. in room B of the Department of Mathematics and Computer Science<\/p>\n Exam<\/strong><\/p>\n The final exam consists in a presentation, and it can be recognized as 3.2 CFR.<\/p>\n References<\/strong><\/p>\n 1. Gidas, B.; Ni, Wei-Ming; Nirenberg, L. Symmetry and related properties via the maximum principle<\/strong>. Commun. Math. Phys. 68, 209-243 (1979). Geometric Analysis Prof. Antonio Greco Dipartimento di Matematica e Informatica Universit\u00e0 degli Studi di Cagliari Abstract The course is an introduction to the problem of\u00a0determining the shape of solutions to boundary-value problems\u00a0for second-order partial differential equations, mainly\u00a0of elliptic type, occasionally parabolic. Outline – Review of the weak maximum principle, the strong maximum principle, and the Hopf lemma. – Some motivations for Geometric Analysis and some characteristic results: the soap bubble theorem (Aleksandrov’s theorem), Serrin’s overdetermined problem, the Gidas-Ni-Nirenberg symmetry result. – Convexity of solutions to the Dirichlet problem. Quasiconvexity. – The Morse index of a solution and its role in […]<\/a><\/p>\n","protected":false},"author":2659,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,10],"tags":[],"class_list":["post-1178","post","type-post","status-publish","format-standard","hentry","category-dipartimento-matematica-informatica","category-events","category-9-id","category-10-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1178","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/users\/2659"}],"replies":[{"embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/comments?post=1178"}],"version-history":[{"count":9,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1178\/revisions"}],"predecessor-version":[{"id":1260,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/posts\/1178\/revisions\/1260"}],"wp:attachment":[{"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/media?parent=1178"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/categories?post=1178"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dottorati.unica.it\/matematicaeinformatica\/wp-json\/wp\/v2\/tags?post=1178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nDipartimento di Matematica e Informatica
\nUniversit\u00e0 degli Studi di Cagliari<\/p>\n
\n– Some motivations for Geometric Analysis and some characteristic results: the soap bubble theorem (Aleksandrov’s theorem), Serrin’s overdetermined problem, the Gidas-Ni-Nirenberg symmetry result.
\n– Convexity of solutions to the Dirichlet problem. Quasiconvexity.
\n– The Morse index of a solution and its role in Geometric Analysis. Work in progress.<\/p>\n
\n2. Berestycki, H.; Nirenberg, L. On the method of moving planes and the sliding method<\/strong>. Bol. Soc. Bras. Mat., Nova S\u00e9r. 22, No. 1, 1-37 (1991).
\n3. Fraenkel, L. E. An introduction to maximum principles and symmetry in elliptic problems<\/strong>. Cambridge University Press. x, 340 p. (2011).
\n4. Protter, Murray H.; Weinberger, Hans F. Maximum principles in differential equations<\/strong>. Prentice-Hall, Inc. X, 261 p. (1967).
\n5. Serrin, James. A symmetry problem in potential theory<\/strong>. Arch. Ration. Mech. Anal. 43, 304-318 (1971).
\n6. Sperb, Rene P. Maximum principles and their applications<\/strong>. Academic Press. IX, 224 p. (1981).<\/p>\n","protected":false},"excerpt":{"rendered":"