Subsolutions and supersolutions in a free boundary problem

Antoine Henrot Laboratoire de Mathématiques, Université de Besançon

TBD mathscidoc:1701.332807

Arkiv for Matematik, 32, (1), 79-98, 1992.7
We begin by giving some results of continuity with respect to the domain for the Dirichlet problem (without any assumption of regularity on the domains). Then, following an idea of A. Beurling, a technique of subsolutions and supersolutions for the so-called quadrature surface free boundary problem is presented. This technique would apply to many free boundary problems in$R$$N$,$N$≥2, which have overdetermined Cauchy data on the free boundary. Some applications to concrete examples are also given.
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  title={Subsolutions and supersolutions in a free boundary problem},
  author={Antoine Henrot},
  booktitle={Arkiv for Matematik},
Antoine Henrot. Subsolutions and supersolutions in a free boundary problem. 1992. Vol. 32. In Arkiv for Matematik. pp.79-98.
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