Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (1): 208-214.doi: 10.1016/S0252-9602(10)60038-0

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LOCAL REGULARITY RESULT IN OBSTACLE PROBLEMS

 GAO Hong-ya, GUO Jing, ZUO Ya-Li, CHU Yu-Ming   

  1. College of Mathematics and Computer Science, Hebei University, Baoding 071002, China
    Hebei Provincial Center of Mathematics, Shijiazhuang 050016, China
  • Received:2006-12-25 Revised:2008-04-21 Online:2010-01-20 Published:2010-01-20
  • Supported by:

    The first author is supported by NSF of Hebei Province (07M003). The fourth author is supported by NSFC (10771195), and NSF of Zhejiang Province (Y607128).

Abstract:

We obtain a local regularity result for solutions to Kψ,θ -obstacle problem of A-harmonic equation divA(x, u(x), ∨ u(x))=0, where A: Ω×R×R→ Rn is a Carath\'eodory function satisfying some coercivity and growth conditions with the natural exponent 1<p<n, the obstacle function ψ≥0$, and the boundary data θ W1, p(Ω).

Key words: local regularity,  A-harmonic equation, obstacle problem

CLC Number: 

  • 35J60
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