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• W2136584228 abstract "Abstract In this paper we consider the problem of prescribing the mean curvature on the boundary of the unit ball of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>R</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:math> , <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>4</mml:mn> </mml:math> . Under the assumption that the prescribed function is flat near its critical point, we give precise estimates on the losses of the compactness, and we provide a new existence result of Bahri-Coron type. Moreover, we establish, under generic boundary condition, a Morse inequality at infinity, which gives a lower bound on the number of solutions to the above problem. MSC: 58E05, 35J65, 53C21, 35B40." @default.
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• W2136584228 date "2013-08-22" @default.
• W2136584228 modified "2023-09-27" @default.
• W2136584228 title "On a geometric equation involving the Sobolev trace critical exponent" @default.
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• W2136584228 doi "https://doi.org/10.1186/1029-242x-2013-405" @default.
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