JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (6): 57-63.doi: 10.6040/j.issn.1671-9352.0.2018.003

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Regularity for solutions of elliptic obstacle problems with subcritical growth

  

  1. Department of Mathematics, Northwestern Polytechnical University, Xian 710129, Shaanxi, China
  • Received:2018-01-08 Online:2018-06-20 Published:2018-06-13

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Abstract: Based on a modification of p-harmonic approximation argument, the gradients of solutions to the quasilinear elliptic p-Laplace type obstacle problems with subcritical growth enjoy the Morrey regularity are proved. Then the Hölder continuity of solutions is obtained by using the integral characterization of Hölder continuous functions. Making use of this method, one can simplify the proof avoiding the proof of a suitable reverse Hölder inequality for the gradient.

Key words: elliptic obstacle problems, lder continuity, Hö, subcritical growth, Morrey regularity

CLC Number: 

  • O175.2
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