2025/10/15 by Kanungo, Suman, Mishra, Pawan Kumar, Bisci, Giovanni Molica
#2020 Mathematics Subject Classification. 35J70 #35A15 #35H20 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.13299
We consider the following nonlocal Brézis-Nirenberg type critical Choquard problem involving the Grushin operator \ \beginaligned -Δγamp; u =λu + (∫Ω\frac|u(w)|^2^*γ, μd(z-w)μdw) |u|^2^*γ, μ-2u amp;amp;in Ω, u amp;= 0 amp;amp;on ∂ Ω, \endaligned . where Ω is an open bounded domain in ℝN, with N ≥ 3, and λ>0 is a parameter. Here, Δγ represents the Grushin operator, defined as Δγu(z) = Δx u(z) +(1+γ)2 |x|2γ Δy u(z), γ≥ 0, where z=(x,y)∈ Ω⊂ ℝm× ℝn, m+n=N ≥ 3 and 2^*γ,μ= (2Nγ-μ)/(Nγ-2) is the Sobolev critical exponent in the Hardy-Littlewood context with Nγ= m+(1+γ)n is the homogeneous dimension associated to the Grushin operator and 0<μ