An eigenvalue problem for a fully nonlinear elliptic equation with gradient constraint

@article{Hynd2014AnEP,
  title={An eigenvalue problem for a fully nonlinear elliptic equation with gradient constraint},
  author={Ryan Hynd},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2014},
  volume={56},
  pages={1-31}
}
  • Ryan Hynd
  • Published 2014
  • Mathematics
  • Calculus of Variations and Partial Differential Equations
We consider the problem of finding $$\lambda \in {\mathbb {R}}$$λ∈R and a function $$u:{\mathbb {R}}^n\rightarrow {\mathbb {R}}$$u:Rn→R that satisfy the PDE $$\begin{aligned} \max \left\{ \lambda + F(D^2u) -f(x),H(Du)\right\} =0, \quad x\in {\mathbb {R}}^n. \end{aligned}$$maxλ+F(D2u)-f(x),H(Du)=0,x∈Rn.Here F is elliptic, positively homogeneous and superadditive, f is convex and superlinear, and H is typically assumed to be convex. Examples of this type of PDE arise in the theory of singular… Expand

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