We prove existence and regularity results for free transmission problems governed by fully nonlinear elliptic equations with nonhomogeneous degeneracies.

In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the quasilinear systems. The serve as important mathematical tools for modelling subgame perfect equilibrium solutions to time-inconsistent dynamic choice problems, which are motivated by study of behavioral economics. Different types were studied but left behind case and connection...

Given a smooth positive function F∈C∞(Sn) such that the square of its 1-homogeneous extension on Rn+1∖{0} is uniformly convex, Wulff shape WF convex body in Euclidean space Rn+1 with F being support boundary ∂WF. In this paper, we introduce fully nonlinear locally constrained anisotropic curvature flow ∂∂tX=(1−Ek1/kσF)νF,k=2,…,nin space, where Ek denotes normalized kth mean respect to WF, σF an...

We study the free boundary of solutions to parabolic obstacle problem with fully nonlinear diffusion. show that splits into a regular and singular part: near points is C∞ in space time. Furthermore, we prove set locally covered by Lipschitz manifold dimension n−1 which also ε-flat space, for any ε>0.