A minimum problem with free boundary for a degenerate quasilinear operator

  • Donatella Danielli
  • Arshak Petrosyan


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: \(J(u)=\int_\Omega\left( |\nabla u|^p + \lambda^p\chi_{\{u>0\}}\right)dx\rightarrow \min\qquad (1<p<\infty).\)


System Theory Minimum Problem Free Boundary Type Minimum Quasilinear Operator 
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© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

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