Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate/singular fully non-linear elliptic equations
By C. Imbert. 2009
81 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b23993b20276d1c00c4b1bd83865fbef796951b8
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In Applied Mathematics
- Luis Silvestre
- C. Imbert
- Russell W. Schwab
- Juan Luis V'azquez
- Enrico Valdinoci
- Xavier Ros-Oton
- Luis Caffarelli
- Pablo Raúl Stinga
In Computational Theory and Mathematics
- Luis Silvestre
- C. Imbert
- Enrico Valdinoci
- Russell W. Schwab
- Xavier Ros-Oton
- Luis Caffarelli
- Pablo Raúl Stinga
- Nestor Guillen
In Mathematical Physics
- C. Imbert
- Luis Silvestre
- Juan Luis V'azquez
- Pablo Raúl Stinga
- Enrico Valdinoci
- C. Bucur
- Jinggang Tan
- Luis Caffarelli
Citations in the corpus
- Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, unknown): “Local Hölder continuity was proven independently in [21] and [25] by means of Alexandroff-Bakelman-Pucci estimate; see also [27] for a much more robust treatment.”
- Estimates on elliptic equations that hold only where the gradient is large (2013, background): “In [11], on the one hand, a Harnack inequality and Hölder estimates are proved for functions satisfying the asumptions of this article.”