A Bernoulli problem with non constant gradient boundary constraint

Chiara Bianchini (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 CORIDA - Robust control of infinite dimensional systems and applications

We present in this paper a result about existence and convexity of solutions to a free boundary problem of Bernoulli type, with non constant gradient boundary constraint depending on the outer unit normal. In particular we prove that, in the convex case, the existence of a subsolution guarantees the existence of a classical solution, which is proved to be convex.

Mots clés: Bernoulli problem; Convexity

Domaines: Equations aux dérivées partielles [math.AP]

Chiara Bianchini. A Bernoulli problem with non constant gradient boundary constraint. 2010. ⟨hal-00543621⟩