Some uniqueness results for Bernoulli interior free-boundary problems in convex domains

More precisely, under certain assumptions, we show that the existence of solutions to appropriate parameterized reverse convex and convex maximization problems implies the existence

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des

We propose a new numerical method for the solution of Bernoulli’s free boundary value problem for harmonic functions in a doubly connected domain D in R 2 where an unknown free

Marcus, Existence theorems for superlinear elliptic Dirichlet problems in exterior domains, in: Nonlinear Functional Analysis and its Applications, Part 1, Berkeley, CA, 1983,

Lieberman, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal. Magenes, Problemi ai limiti

We first reformulate the free boundary problem into a fixed conormal boundary value problem for a nonlinear elliptic equation of second order in unbounded domains and then

- Using the layer potentials theory and the properties of the singular fundamental solution we obtain a regularity theorem in Sobolev spaces for solutions of

[2] Andrew Acker, Antoine Henrot, Michael Poghosyan, Henrik Shahgholian, The multi-layer free boundary problem for the p-Laplacian in convex domains, Interface.. Sabidussi