On Axially Symmetric Solutions of Fully Nonlinear Elliptic Equations

@inproceedings{Nadirashvili2010OnAS,
  title={On Axially Symmetric Solutions of Fully Nonlinear Elliptic Equations},
  author={Nikolai S. Nadirashvili and Serge Vladuts},
  year={2010}
}
Here, uij denotes the partial derivative ∂ u/∂xi∂xj . A function u is called a classical solution of (1) if u ∈ C(Ω) and u satisfies (1). Actually, any classical solution of (1) is a smooth (C) solution, provided that F is a smooth (C) function of its arguments. For a matrix S ∈ S(R) we denote by λ(S) = {λi : λ1 ≤ ... ≤ λn} ∈ R the (ordered) set of eigenvalues of the matrix S. Equation (1) is called a Hessian equation ([T1],[T2] cf. [CNS]) if the function F (S) depends only on the eigenvalues… 
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