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

Nassif Ghoussoub, Frédéric Robert
2009 Transactions of the American Mathematical Society  
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
more » ... osition of the subspace ⊥ , the orthogonal of , with respect to the domain Ω, as well as on the curvature of the boundary ∂Ω at its points of intersection with ⊥ .
doi:10.1090/s0002-9947-09-04655-8 fatcat:dq5pmqmjivbprlbks3hrsfilby