Corpus ID: 237940232

How to construct parametrized families of free boundaries near nondegenerate solutions

  title={How to construct parametrized families of free boundaries near nondegenerate solutions},
  author={Lorenzo Cavallina},
In this paper, we introduce the notion of variational free boundary problem. Namely, we say that a free boundary problem is variational if its solutions can be characterized as the critical points of some shape functional. Moreover, we extend the notion of nondegeneracy of a critical point to this setting. As a result, we provide a unified functional-analytical framework that allows us to construct families of solutions to variational free boundary problems whenever the shape functional is… Expand

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