A Bernoulli problem with non constant gradient boundary constraint

Details A Bernoulli problem with non constant gradient boundary constraint A Bernoulli problem with non constant gradient boundary constraint

2010-09-07

arxiv.org/abs/1009.1277v1

Mathematics

Analysis of PDEs

8 pages, no figures

Scientific paper

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.

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