Mean curvature ow with obstacles: existence, uniqueness and regularity of solutions
نویسندگان
چکیده
We show short time existence and uniqueness of C solutions to the mean curvature ow with obstacles, when the obstacles are of class C. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface.
منابع مشابه
Mean curvature flow with obstacles: existence, uniqueness and regularity of solutions
We show short time existence and uniqueness of C solutions to the mean curvature flow with obstacles, when the obstacles are of class C. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface.
متن کاملMean curvature flow with obstacles
We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme. Assuming the regularity of the obstacles, in the two-dimensional case we show existence and uniqueness of a regular solution before the onset of singularities. Finally, we discuss a...
متن کاملThe volume preserving crystalline mean curvature ow of convex sets in R
We prove the existence of a volume preserving crystalline mean curvature at ow starting from a compact convex set C ⊂ R and its convergence, modulo a time-dependent translation, to a Wul shape with the corresponding volume. We also prove that if C satis es an interior ball condition (the ball being the Wul shape), then the evolving convex set satis es a similar condition for some time. To prove...
متن کاملRegularity for obstacle problems in infinite dimensional Hilbert spaces
In this paper we study fully nonlinear obstacle type problems in Hilbert spaces. We introduce the notion of Q-elliptic equation and prove existence, uniqueness, and regularity of viscosity solutions of Q-elliptic obstacle problems. In particular we show that solutions of concave problems with semiconvex obstacles are in the space W 2,∞ Q .
متن کاملExistence and Regularity for the Generalized Mean Curvature Flow Equations
X iv :0 90 8. 30 57 v1 [ m at h. A P] 2 1 A ug 2 00 9 EXISTENCE AND REGULARITY FOR THE GENERALIZED MEAN CURVATURE FLOW EQUATIONS RONGLI HUANG AND JIGUANG BAO Abstract. By making use of the approximation method, we obtain the existence and regularity of the viscosity solutions for the generalized mean curvature flow. The asymptotic behavior of the flow is also considered. In particular, the Diri...
متن کامل