{"id":138,"date":"2022-04-08T17:56:40","date_gmt":"2022-04-08T21:56:40","guid":{"rendered":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/?p=138"},"modified":"2022-05-01T10:09:18","modified_gmt":"2022-05-01T14:09:18","slug":"tba-2","status":"publish","type":"post","link":"https:\/\/dev.eventos.cmm.uchile.cl\/pdeseminar\/2022\/04\/tba-2\/","title":{"rendered":"Optimal design problems for a degenerate operator in Orlicz-Sobolev spaces"},"content":{"rendered":"

Speaker: Jefferson Abrantes<\/a><\/h3>\n

Universidade Federal de Campina Grande, Brazil<\/h3>\n

Date:\u00a0 April 26, 2022 at 12 Santiago time<\/h3>\n

Abstract: An optimization problem with volume constraint involving the \\(\\Phi\\)-Laplacian in Orlicz-Sobolev spaces is considered for the case where \\(\\Phi\\) does not satisfy the natural condition introduced by Lieberman. A minimizer \\(u_\\Phi\\) having non-degeneracy at the free boundary is proved to exist and some important consequences are established like the Lipschitz regularity of \\(u_\\Phi\\) along the free boundary, that the set \\(\\{u_\\Phi >0\\}\\) has uniform positive density, that the free boundary is porous with porosity \\(\\delta>0\\) and has finite \\((N-\\delta)\\)-Hausdorff measure. Under a geometric compatibility condition set up by Rossi and Teixeira, it is established the behavior of a \\(\\ell\\)-quasilinear optimal design problem with volume constraint for \\(\\ell\\) small. As \\(\\ell \\to 0^+\\), we obtain a limiting free boundary problem driven by the infinity-Laplacian operator and find the optimal shape for the limiting problem. The proof is based on a penalization technique and a truncated minimization problem in terms of the Taylor polynomial of \\(u_\\Phi\\).<\/p>\n

Venue:<\/strong> Online via Zoom \/ Sala de seminarios DIM, Beauchef 851, piso 5
\nChair:<\/strong> Gabrielle Nornberg<\/p>\n<\/i> YouTube video (in English)<\/span><\/a>\n

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