Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations

Abstract

In this paper, we study fully non-linear elliptic equations in non-divergence form which can be degenerate when "the gradient is small". Typical examples are either equations involving the $m$-Laplace operator or Bellman-Isaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such degenerate elliptic equations.

27 pages. To appear in JDE

References in corpus (1)

• Eigenfunctions for singular fully non linear equations in unbounded domains

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• Approximation by mappings with singular Hessian minors
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• Optimal C^{1,\apha} regularity for degenerate fully nonlinear elliptic equations with Neumann boundary condition
• Radó- type theorem for subharmonic and plurisubharmonic functions
• Regularity of solutions to degenerate fully nonlinear elliptic equations with variable exponent