Convergence of nonlocal geometric flows to anisotropic mean curvature motion

Abstract: We consider the Cauchy problem for motions by nonlocal curvature, whose well-posedness may be established in the framework of viscosity solutions. We show that a suitable rescaling of the nonlocal curvature induces a localisation effect, that is, as the scaling parameter tends to 0, we retrieve an anisotropic mean curvature functional. From this fact, thanks to the theory of geometric barriers by De Giorgi, we prove that the solutions to the rescaled nonlocal motions locally uniformly converge to the solution of the local flow. The talk is based on joint work with A. Cesaroni (Padova).

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).