cvgmt Seminarshttps://cvgmt.sns.it/seminars/en-usTue, 24 Nov 2020 04:31:18 +0000Sobolev calculus on weighted Euclidean spaceshttps://cvgmt.sns.it/seminar/766/2020-11-25: <a href="/person/2482/">D. Lučić</a>.<p>In order to join the seminar, please fill in the <a href='https://forms.gle/owiZHxjH2V9cUyqJ8'>mandatory participation form</a> before November 24th. Further information and instructions will be sent afterwards to the online audience.</p><p>The study of the Sobolev space over weighted Euclidean spaces(i.e. equipped with an arbitrary Radon measure) has been initiated inthe late nineties, motivated by various applications in the field of theCalculus of Variations. Two important approaches were introduced by Bouchitté-Buttazzo-Seppecher and Zhikov, both relying upon a notion of'Sobolev tangent bundle'. In this talk, we will prove the equivalenceof these two theories, by employing a third notion of Sobolev spacedue to Ambrosio-Gigli-Savaré, which comes from the more general settingof analysis on metric measure spaces. Moreover, we will investigatethe relation between the above-mentioned 'Sobolev tangent bundle' andthe 'Lipschitz tangent bundle' introduced by Alberti-Marchese. Finally,we will provide necessary and sufficient conditions for the Sobolev-Lipschitztangent bundles to have full rank.</p>https://cvgmt.sns.it/seminar/766/Concentration versus oscillation effects in brittle damagehttps://cvgmt.sns.it/seminar/764/2020-11-26: J. F. Babadjian.<p>This talk is concerned with the asymptotic analysis of a variational model of brittle damage, when the damaged zone concentrates into a set of zero Lebesgue measure, and, at the same time, the stiffness of the damaged material becomes arbitrarily small. In a particular non-trivial regime, concentration leads to a limit energy with linear growth as typically encountered in perfect plasticity. While the singular part of the limit energy can be easily described, the identification of the bulk part of the limit energy requires a subtler analysis of the interplay between concentration and oscillation properties of the displacements. This is a joint work with F. Iurlano and F. Rindler.</p>https://cvgmt.sns.it/seminar/764/Contact surface of Cheeger setshttps://cvgmt.sns.it/seminar/765/2020-11-26: <a href="/person/1714/">M. Caroccia</a>.<p>Geometrical properties of Cheeger sets have been deeply studied by many authors since their introduction, as a way of bounding from below the first Dirichlet (p)-Laplacian eigenvualue. They represents the first eigenfunction of the Dirichlet (1)-Laplacian of a domain. In this talk we will introduce a recent property, studied in collaboration with Simone Ciani, concerning their contact surface with the ambient space. In particular we will show that the contact surface cannot be too small, with a lower bound on the dimension strictly related to the regularity of the ambient space. The talk will focus on the introduction of the problem and with a brief explanation of its connection with the Diri chlet (p)-Laplacian eigenvalue problem. Then a brief sketch of the proof is given. Functional to the whole argument is the notion of removable singularity, as a tool for extending solutions of pdes under some regularity constraint.</p>https://cvgmt.sns.it/seminar/765/