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A minimum problem with free boundary for a degenerate quasilinear operator

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Abstract.

In this paper we prove \(C^{1,\alpha}\) regularity (near flat points) of the free boundary \(\partial\{u > 0\}\cap\Omega\) in the Alt-Caffarelli type minimum problem for the p-Laplace operator: \(J(u)=\int_\Omega\left( |\nabla u|^p + \lambda^p\chi_{\{u>0\}}\right)dx\rightarrow \min\qquad (1<p<\infty).\)

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, IN 47907, West Lafayette, USA

    Donatella Danielli

  2. Department of Mathematics, University of Texas at Austin, TX 78712, Austin, USA

    Arshak Petrosyan

Authors
  1. Donatella Danielli
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  2. Arshak Petrosyan
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Correspondence to Donatella Danielli.

Additional information

Received: 3 June 2003, Accepted: 9 June 2004, Published online: 8 February 2005

Mathematics Subject Classification (2000):

35R35, 35J60

The first author is partially supported by NSF Grant DMS-0202801 and NSF CAREER Grant DMS-0239771

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Danielli, D., Petrosyan, A. A minimum problem with free boundary for a degenerate quasilinear operator. Calc. Var. 23, 97–124 (2005). https://doi.org/10.1007/s00526-004-0294-5

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  • DOI: https://doi.org/10.1007/s00526-004-0294-5

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