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, Volume 94, Issue 1, pp 151–167 | Cite as

Local a priori estimates in Lp for first order linear operators with nonsmooth coefficients

  • Jorge Hounie
  • Maria Eulália Moraes Melo
Article

Abstract

We prove local a priori estimates inL p , 1<p<∞, for first-order linear operators that satisfy the Nirenberg-Treves condition (p) and whose coefficients have Lipschitz continuous derivatives of order one. When the number of variables is two, only Lipschitz continuity of the coefficients is assumed. This extends toL p spaces estimates that were previously known forp=2. Examples show that the regularity required from the coefficients is essentially minimal.

Keywords

Lipschitz Function Lipschitz Continuity Principal Symbol Principal Type Local Solvability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Jorge Hounie
    • 1
  • Maria Eulália Moraes Melo
    • 1
    • 2
  1. 1.Departamento de MatemáticaUniv. Fed. de São CarlosSão Carlos, SPBrasil
  2. 2.Recife, PEBrasil

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