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Onil90
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A liouvilleLiouville theorem for a uniformly elliptic equation in divergence form

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Onil90
  • 823
  • 4
  • 9

A liouville theorem for a uniformly elliptic equation in divergence form

I would like to know if there exists a Liouville theorem for solutions $u : \mathbb{R}^n \to \mathbb{R}$ of uniformly elliptic equations of the kind $$ D_i \left( a_{ij} D_j u \right) + b_i D_i u = 0. $$ I assume the coefficients $a_{ij},b_i \in C^{\infty}(\mathbb R^n) \cap L^{\infty}(\mathbb{R}^n)$.

Any hint/reference would be highly appreciated!