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• W1709282685 abstract "Our objective, here, is to generalize our earlier results on the existence of classical convex solution to a free boundary problem with a Bernoulli-type boundary gradient condition and with the $p$-Laplacian as the governing operator. The main theorems of this paper assert that the exterior and the interior free boundary problem with a Bernoulli law, i.e. with a prescribed pressure $a(x)$ on the “free” streamline of the flow, have convex solutions provided the initial domains are convex. The continuous function $a(x)$ is subject to certain convexity properties. In our earlier results we have considered the case of constant $a(x)$. In the lines of the proof of the main results we also prove the semi-continuity (up to the boundary) of the gradient of the $p$-capacitary potentials in convex rings, with $C^1$ boundaries." @default.
• W1709282685 created "2016-06-24" @default.
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• W1709282685 date "2002-02-14" @default.
• W1709282685 modified "2023-09-30" @default.
• W1709282685 title "The one phase free boundary problem for the $p$-Laplacian with non-constant Bernoulli boundary condition" @default.
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• W1709282685 doi "https://doi.org/10.1090/s0002-9947-02-02892-1" @default.
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