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The final case of unduloids is more complex. All unduloids of dimension two through seven are unstable, but there exists stable unduloids of dimension nine and greater. In this talk, we will consider the missing case of whether there exists stable unduloids of dimension eight. We will also work towards finding a criterion to determine if a specific unduloid is stable or unstable.
In this talk, we are going to higher order convergence in Homogenization process through higher order interior and boundary correctors in various Nonlinear equations. Similar issues arises in vanishing viscous Hamiltonian Equations and Lower order convergence in Parabolic problems with various space and time scales. We also discuss how this idea can be applied to the other problem where some parameters approaches to zero: for example diffusive limit in Kinetic theory, asymptotic limit in parabolic flows, and so on. In , Cheeger established lower bounds on the first eigenvalue of the Laplacian on compact Riemannian manifolds in terms of a certain isoperimetric problem.
The analogous problem on domains of Euclidean space has generated much interest in recent years, due in part to its connections to capillarity theory, image processing, and landslide modeling. In this talk, based on joint work with Leonardi and Saracco, we give an explicit characterization of minimizers in this isoperimetric problem for a very general class of planar domains. In order to do this we will study non-differentiable, and possibly unbounded functionals.
Part of the presented results have been obtained in collaboration with Marco Squassina and Lucio Boccardo.
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I will review some old and new results concerning existence, multiplicity and asymptotic behaviour of solutions to the classical Lane-Emden equation on a planar domain when the exponent of the non-linearity is large. Derek W. Robinson Australian National University, Australia. Uniqueness depends on geometric properties, e. These effects are both important for uniqueness of the process. This result is valid with mild regularity restrictions on the boundary and applies to Lipschitz domains and a wide class of domains with fractal boundaries.
Weissler and H. Brezis - T. Cazenave; furthermore, non-uniqueness results for certain singular initial data were given by W. Sacks and E. Trudinger - J. With prove that similar phenomena, namely existence, non-existence and non-uniqueness, occur for suitable exponential nonlinearities and singular initial data in certain Orlicz spaces. Critical points of eigenvalues with respect to the metric of differential operators in fixed area surfaces are important objects to understand the geometry and topology of surfaces, after the program initiated by Yau and collaborators.
I will describe several results related to existence and regularity of extremal metrics for any eigenvalue of the Laplace-Beltrami on smooth surfaces. Then I will move on to their characterizations as generating minimal immersions by eigenvectors into round spheres. I will describe also several applications to isoperimetric inequalities on the 2-sphere. I will finally describe recent results in higher dimensions and some open problems in the complex case. This equation arises in stochastic control theory, as well as in KPZ type models for interface growth in ballistic deposition processes, and it constitutes a model case of parabolic equations with first order nonlinearity.
The solutions display a variety of interesting behaviors and we will discuss two classes of phenomena: Gradient blow-up GBU : localization of singularities on the boundary, single-point GBU, Bernstein estimates, time rate of GBU, spatial GBU profiles. Continuation in the viscosity sense after GBU : solutions with and without loss of boundary conditions, recovery of boundary conditions, regularization. We study the local structure and the regularity of free boundaries of segregated critical configurations involving the square root of the laplacian.
We develop an improvement of flatness theory and, as a consequence of this and Almgren's monotonicity formula, we obtain partial regularity up to a small dimensional set of the nodal set, thus extending the known results by Caffarelli and Lin, Tavares and Terracini for the standard diffusion to some anomalous case. Please send an email to? This event has especially the intention to give PhD students and early career researchers ECR the opportunity to meet some of the leading experts in the field of nonlinear partial differential equations.
agendapop.cl/wp-content/mspy/jem-como-rastrear-um.php The participation of each ECR at this workshop is warmly welcomed. Contact the University Disclaimer Privacy Accessibility. Library Current students Staff intranet. School of Mathematics and Statistics.
The workshop will be held at the University of Sydney in the new Buidling F See also the information on how to get there. About this page. For questions or comments please contact webmaster maths. Non-concavity of the Robin ground state Ben Andrews Australian National University, Australia Abstract I will discuss recent work joint with Julie Clutterbuck Monash and Daniel Hauer Sydney in which we show that the first eigenfunction for the Robin problem on a convex domain is in general not log-concave, and indeed may even have non-convex super level sets.
Diffusion with non-local boundary conditions Wolfgang Arendt University of Ulm, Germany Abstract Non-local boundary conditions have occur if we tell a particle reaching the boundary to go back in the interior of the domain with a certain probability.