Starts 18 Feb 2021 14:00
Ends 18 Feb 2021 15:00
Central European Time
Search
Search in Conferences:
Math Associates Seminar: Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian
Zoom Meeting
Register in advance for this meeting:
After registering, you will receive a confirmation email containing information about joining the meeting.
Abstract: In this talk we will present some potential-theoretic aspects of the eikonal and infinity Laplace operator on a Finsler manifold M. Our main result shows that the forward completeness of M can be detected in terms of Liouville properties and maximum principles at infinity for subsolutions of suitable in homogeneous inequalities. Also, an ∞-capacity criterion and a viscosity version of Ekeland principle are proved to be equivalent to the forward completeness of M. Part of the proof hinges on a new boundary-to-interior Lipschitz estimate for solutions of an inhomogeneous equation for the infinity Laplacian on compact sets, that implies a uniform Lipschitz estimate for certain entire, bounded solutions without requiring the completeness of M.
Joint work with Damião J Araújo, Luciano Mari.
Abstract: In this talk we will present some potential-theoretic aspects of the eikonal and infinity Laplace operator on a Finsler manifold M. Our main result shows that the forward completeness of M can be detected in terms of Liouville properties and maximum principles at infinity for subsolutions of suitable in homogeneous inequalities. Also, an ∞-capacity criterion and a viscosity version of Ekeland principle are proved to be equivalent to the forward completeness of M. Part of the proof hinges on a new boundary-to-interior Lipschitz estimate for solutions of an inhomogeneous equation for the infinity Laplacian on compact sets, that implies a uniform Lipschitz estimate for certain entire, bounded solutions without requiring the completeness of M.
Joint work with Damião J Araújo, Luciano Mari.