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Elliptic equations with critical growth and a large set of boundary singularities

2009
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Transactions of the American Mathematical Society
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We solve variationally certain equations of stellar dynamics of the in a domain Ω of ℝ , where is a proper linear subspace of ℝ . Existence problems are related to the question of attainability of the best constant in the following inequality due to Maz'ya (1985) : where 0 < < 2, 2 ★ ( ) = 2( − ) −2 and where is the orthogonal projection on a linear space , where dim ℝ ≥ 2 (see also Badiale-Tarantello (2002) ). We investigate this question and how it depends on the relative position of the

doi:10.1090/s0002-9947-09-04655-8
fatcat:dq5pmqmjivbprlbks3hrsfilby