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Harnack Inequalities and ABP Estimates for Nonlinear Second‐Order Elliptic Equations in Unbounded Domains

Author

Listed:
  • M. E. Amendola
  • L. Rossi
  • A. Vitolo

Abstract

We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary. As applications, we deduce ABP‐type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville‐type theorem.

Suggested Citation

  • M. E. Amendola & L. Rossi & A. Vitolo, 2008. "Harnack Inequalities and ABP Estimates for Nonlinear Second‐Order Elliptic Equations in Unbounded Domains," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    • Handle: RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:178534
    DOI: 10.1155/2008/178534
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    References listed on IDEAS

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    1. Murray H. Protter & Hans F. Weinberger, 1984. "Maximum Principles in Differential Equations," Springer Books, Springer, number 978-1-4612-5282-5, March.
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