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In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of $\R^n$, $n\geq 3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function $H(x)$ is $\beta\in ]1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.
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참고문헌 (13)
참고문헌 신청
W. Abdelhedi / 2010 / Prescribing mean curvature on Bn / Internat. J. Math 21(9):1157~1187
W. Abdelhedi / 2009 / Conformal metrics with prescribed boundary mean curvature on balls / Ann. Global Anal. Geom 36(4):327~362
M. A. Al-Ghamdi / 2013 / On a geometric equation involving the Sobolev trace critical exponent / J. Inequal. Appl 2013(405):25
M. A. Al-Ghamdi / 2014 / Topological methods for boundary mean curvature problem on B n / Adv. Nonlinear Stud 14(2):445~461
A. Bahri / 1989 / Critical point at infinity in some variational problems / Longman Sci. Tech. Harlow
W. Abdelhedi / 2009 / Conformal metrics with prescribed boundary mean curvature on balls / Ann. Global Anal. Geom 36(4):327~362
M. A. Al-Ghamdi / 2013 / On a geometric equation involving the Sobolev trace critical exponent / J. Inequal. Appl 2013(405):25
M. A. Al-Ghamdi / 2014 / Topological methods for boundary mean curvature problem on B n / Adv. Nonlinear Stud 14(2):445~461
A. Bahri / 1989 / Critical point at infinity in some variational problems / Longman Sci. Tech. Harlow
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