Vector fields method establishes a Liouville-type theorem for quasilinear p-Laplace equations, revealing implications for conormal boundary conditions.
We use the method of vector fields to obtain a Liouville-type theorem for a class of quasilinear p-Laplace type equations with conormal boundary condition in the half space. These p-Laplace type equations are the subcritical case of the Euler-Lagrange equation of the Sobolev trace inequality in the half space.
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Bao et al. (2025) studied this question.
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