CVGMT Seminarshttp://cvgmt.sns.it/seminars/en-usFri, 25 May 2018 03:23:30 +0000Uniqueness and existence results via Morse index for Lane Emden problemshttp://cvgmt.sns.it/seminar/644/2018-05-29: F. De Marchis.<p>We consider the classical Lane Emden equation in bounded domains of the plane with Dirichlet boundary conditions and we present some results concerning the Morse index of solutions to this problem, when the exponent of the nonlinearity is large. Via these Morse index computations and a precise asymptotic analysis we can deduce a uniqueness result for positive solutions in convex domains and also some existence results of non-radial sign-changing solutions in the ball. Based on joint papers with M. Grossi, I. Ianni and F. Pacella.</p>http://cvgmt.sns.it/seminar/644/Properties of Convex sets in Wiener spaceshttp://cvgmt.sns.it/seminar/643/2018-05-30: M. J. Miranda.<p>We show some recent results on convex sets in Wiener spaces. We characterize the essential and reduced boundary ofopen convex sets and investigate integration by parts formulae. Of particular interest is the investigation of trace theoremsfor functions of bouned variation on boundaries of subsets in Wiener spaces.</p>http://cvgmt.sns.it/seminar/643/A nonlocal isoperimetric problem with dipolar repulsionhttp://cvgmt.sns.it/seminar/642/2018-06-06: S. Thilo.<p>We study a functional in which perimeter and regularized dipolar repulsion compete under a volume constraint.</p><p>In contrast to previously studied similar problems, the nonlocal term contributes to the perimeter term to leading order for small regularization parameters.</p><p>Indeed, below a critical value for the dipolar strength, the limiting functional is a renormalized perimeter and for small, positive regularization parameters the minimizers are balls.At critical dipolar strength, we identify the next-order Gamma-limit and prove that a continuous pertubation of the problem has non-spherical minimizers for some masses.</p><p>Furthermore, for a wide class of nonlocal isoperimetric problems, we establish existence of generalized minimizers by interpreting them as minimizers of suitably relaxed functionals.</p>http://cvgmt.sns.it/seminar/642/Well-posedness of ODE's in metric measure spaceshttp://cvgmt.sns.it/seminar/634/2018-09-24: <a href="/person/3/">L. Ambrosio</a>.http://cvgmt.sns.it/seminar/634/The isoperimetric problem in the Euclidean space with densitieshttp://cvgmt.sns.it/seminar/635/2018-09-24: <a href="/person/151/">A. Pratelli</a>.http://cvgmt.sns.it/seminar/635/How a minimal surface leaves a thin obstaclehttp://cvgmt.sns.it/seminar/636/2018-09-24: E. Spadaro.http://cvgmt.sns.it/seminar/636/