A Fefferman-Phong Type Inequality and Applications to Quasilinear Subelliptic Equations

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Abstract

We establish a nonlocal generalization of a well-known inequality by C. Fefferman and D. H. Phong (equation presented) for u ∈ C0(ℝn) and V belonging to the Morrey space Ms,2sn with 1 < s ≤ n/2, when the gradient in the right-hand side is replaced by the energy associated to an arbitrary system of Lipschitz continuous vector fields. Accordingly, the multiplier V is taken in an appropriate Morrey space defined using the Carnot-Carathéodory metric generated by the vector fields. As an application, we prove the Harnack inequality and the Hölder continuity of solutions for a wide class of second order quasilinear subelliptic equations.

Original languageEnglish (US)
Pages (from-to)387-413
Number of pages27
JournalPotential Analysis
Volume11
Issue number4
DOIs
StatePublished - 1999
Externally publishedYes

Keywords

  • Fefferman-Phong inequality
  • Harnack inequality
  • Morrey spaces
  • Subelliptic equations

ASJC Scopus subject areas

  • Analysis

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