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A remark on the two-phase obstacle-type problem for the p-Laplacian

  • Jun Zheng EMAIL logo , Binhua Feng and Peihao Zhao
Published/Copyright: May 5, 2017

Abstract

In this paper, we give a remark on the two-phase obstacle-type problem for the p-Laplacian when 1<p<2 and p is close to 2. We prove that the free boundary where the gradient vanishes has locally finite (n-1)-Hausdorff measure.

MSC 2010: 35R35; 35J75; 35J92

Communicated by Frank Duzaar


Funding statement: This work is partially supported by the Fundamental Research Funds for the Central Universities: No. 10801B10096018 and No. 10801X10096022.

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Received: 2015-11-23
Revised: 2017-04-19
Accepted: 2017-04-20
Published Online: 2017-05-05
Published in Print: 2018-07-01

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