For the Grushin-type operator L, the inequality |Ω|^{(Q-1)/Q} ≤ C P(Ω) holds for smooth bounded domains Ω in R^{n+m}, where Q = [n + m(β + 1 - α)] / (1 - α).
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Isoperimetric Inequality for degenerate elliptic operators of Grushin type
For the Grushin-type operator L, the inequality |Ω|^{(Q-1)/Q} ≤ C P(Ω) holds for smooth bounded domains Ω in R^{n+m}, where Q = [n + m(β + 1 - α)] / (1 - α).