A Non-Linear problem involving critical Sobolev exponent
نویسندگان
چکیده
We study the non-linear minimization problem on H 0 (Ω) ⊂ L q with q = 2n n−2 : inf ‖u‖ Lq =1 ∫ Ω (1 + |x| |u|)|∇u|. We show that minimizers exist only in the range β < kn/q which corresponds to a dominant nonlinear term. On the contrary, the linear influence for β ≥ kn/q prevents their existence.
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