Geodesic
Some geometric and analytic properties of solutions of Bernoulli free-boundary problems
Eugen Varvaruca1
1University of Bath, United Kingdom
Interfaces and free boundaries, Tome 9 (2007) no. 3, pp. 367-381

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DOI

A Bernoulli free-boundary problem is one of finding domains in the plane on which a harmonic function simultaneously satisfies linear homogeneous Dirichlet and inhomogeneous Neumann boundary conditions. For a general class of Bernoulli problems, we prove that any free boundary, possibly with many singularities, is necessarily the graph of a function. Also investigated are convexity and monotonicity properties of free boundaries. In addition, we obtain some optimal estimates on the gradient of the harmonic function in question.
DOI : 10.4171/ifb/169
Classification : 35-XX, 65-XX, 76-XX, 92-XX

Eugen Varvaruca  1

1 University of Bath, United Kingdom 
Eugen Varvaruca. Some geometric and analytic properties of solutions of Bernoulli free-boundary problems. Interfaces and free boundaries, Tome 9 (2007) no. 3, pp. 367-381. doi: 10.4171/ifb/169
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     title = {Some geometric and analytic properties of solutions of {Bernoulli} free-boundary problems},
     journal = {Interfaces and free boundaries},
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     year = {2007},
     volume = {9},
     number = {3},
     doi = {10.4171/ifb/169},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/169/}
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