This paper concerns a priori second order derivative estimates of solutions the Neumann problem for Monge-Amp\`ere type equations in bounded domains n dimensional Euclidean space. We first establish double normal estimate on boundary under an appropriate notion domain convexity. Then, assuming barrier condition linearized operator, we provide complete proof global elliptic solutions, as previou...

We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from C0 estimates. Also, the method is flexible and can be applied to a large class of equations. Let (M, g) be a smooth Riemannian manifold of dimension n ≥ 2. We are interested in a priori estimates for solutions of some...

The Monge-Ampere equation, plays a central role in the theory of fully non linear equations. In fact we will like to show how the Monge-Ainpere equation, links in some way the ideas comming from the calculus of variations and those of the theory of fully non linear equations. 2000 Mathematics Subject Classification: 35J15, 35J20, 35J70. When learning complex analysis, it was a remarkable fact t...

Recent gyrokinetic stability calculations have revealed that the spherical tokamak is susceptible to tearing parity instabilities with length scales of a few ion Larmor radii perpendicular to the magnetic field lines. Here we investigate this ‘micro-tearing’ mode in greater detail to uncover its key characteristics and compare it with existing theoretical models of the phenomenon. This has been...

0 < λ ≤ f ≤ Λ in Ω, and for some x ∈ Ω, Sh(x) ⊂⊂ Ω, then Sh(x) is equivalent to an ellipsoid centered at x i.e. kE ⊂ Sh(x)− x ⊂ k−1E for some ellipsoid E of volume h and for a constant k > 0 which depends only on λ,Λ, n. This property provides compactness of sections modulo affine transformations. This is particularly useful when dealing with interior C and W 2,p estimates of strictly convex so...