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

  title={Principal Eigenvalues and an Anti-maximum Principle for Homogeneous Fully Nonlinear Elliptic Equations},
  author={S Armstrong},
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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Hopf’s lemma and anti-maximum principle in general domains

  • I. Birindelli
  • J. Differential Equations 119
  • 1995
Highly Influential
7 Excerpts

The principle eigenvalue and maximum principle for second order elliptic operators in general domains

  • H. Berestycki, L. Nirenberg, S. Varadhan
  • Comm. Pure. Appl. Math 47 (1)
  • 1994
Highly Influential
9 Excerpts

An anti-maximum principle for second-order elliptic operators

  • P. Clément, L. A. Peletier
  • J. Differential Equations 34 (2)
  • 1979
Highly Influential
5 Excerpts

On some nonlinear Sturm-Liouville problems

  • H. Berestycki
  • J. Differential Equations 26 (3)
  • 1977
Highly Influential
12 Excerpts

On the principle eigenvalues and the Dirichlet problem for fully nonlinear operators

  • A. Quaas, B. Sirakov
  • C. R. Acad. Sci. Paris 342
  • 2006
Highly Influential
7 Excerpts

Interior a priori estimates for solutions of fully nonlinear equations

  • L. A. Caffarelli
  • Ann. of Math. (2) 130 (1)
  • 1989
Highly Influential
4 Excerpts

Bifurcation and optimal stochastic control

  • P.-L. Lions
  • Nonlinear Anal. 7 (2)
  • 1983
Highly Influential
7 Excerpts

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