Principal Eigenvalues and an Anti-maximum Principle for Homogeneous Fully Nonlinear Elliptic Equations

@inproceedings{Armstrong2008PrincipalEA,
  title={Principal Eigenvalues and an Anti-maximum Principle for Homogeneous Fully Nonlinear Elliptic Equations},
  author={S Armstrong},
  year={2008}
}
We study the fully nonlinear elliptic equation F (Du, Du, u, x) = f in a smooth bounded domain Ω, under the assumption the nonlinearity F is uniformly elliptic and both positively homogeneous and concave (or convex), jointly in its first three arguments, but does not satisfy a comparison principle. Recently, Quaas and Sirakov [27] demonstrated the existence of two principal “half” eigenvalues for such operators and showed that F satisfies the comparison principle (and hence the Dirichlet… CONTINUE READING

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