Nonlinear operators and differential equations in Banach spaces
Nonlinear operators and differential equations in Banach spaces
Viability theory
Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity
Journal of Mathematical Imaging and Vision
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We present a method for solving the Transport equation when its solution has to belong to a constrained set which is not required to be convex. An autonomous formulation of the characteristics method allows us to use the tangency condition which has been introduced for ordinary differential equations. Thus we obtain a sufficient condition for existence of solutions, which shows the interplay between the geometry of the constraints set K and the velocity field @b. A numerical method is proposed for solving the problem when the sufficient condition is not satisfied. A numerical experiment is presented showing the efficiency of the algorithm proposed.