Acta mathematica scientia,Series A ›› 2017, Vol. 37 ›› Issue (1): 122-145.

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Higher Integrability for Very Weak Solutions of Obstacle Problems to Nonlinear Subelliptic Equations

Du Guangwei, Niu Pengcheng   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129
  • Received:2016-06-21 Revised:2016-11-20 Online:2017-02-26 Published:2017-02-26
  • Supported by:

    Supported by the NSFC (11271299)

Abstract:

In this paper we first establish the local higher integrability for very weak solutions of the Kψ, u0r-obstacle problems to the nonlinear subelliptic equations constructed by Hörmander vector fields which implies the very weak solutions are classical weak solutions. As an application, the compactness results are obtained. We also derive the global higher integrability for very weak solutions of the Kψ, u0r-obstacle problems with a capacitary condition on Ω.

Key words: Nonlinear subelliptic equation, Obstacle problem, Very weak solutions, Higher integrability, Compactness result

CLC Number: 

  • O175.2
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