ON THE PRESCRIBED MEAN CURVATURE PROBLEM ON THE STANDARD n-DIMENSIONAL BALL

Title & Authors
ON THE PRESCRIBED MEAN CURVATURE PROBLEM ON THE STANDARD n-DIMENSIONAL BALL
Bensouf, Aymen;

Abstract
In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of $\small{{\mathbb{R}}^n}$, $\small{n{\geq}3}$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is $\small{{\beta}{\in}[1,n-2]}$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.
Keywords
boundary mean curvature;variational method;loss of compactness;$\small{{\beta}}$-flatness condition;critical point at infinity;
Language
English
Cited by
1.
On the boundary mean curvature equation on B n $\mathbb{B}^{n}$, Boundary Value Problems, 2016, 2016, 1
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