We investigate Liouville-type theorems for elliptic equations with a drift and with a potential posed in bounded domains. We provide sufficient conditions on the potential and on the drift term in order to the equation does not admit nontrivial bounded solutions. We also show that such conditions are optimal. Indeed, when they fail, the elliptic equation possesses infinitely many bounded solutions.
A Liouville-type theorem for elliptic equations with singular coefficients in bounded domains
Biagi S.;Punzo F.
2023-01-01
Abstract
We investigate Liouville-type theorems for elliptic equations with a drift and with a potential posed in bounded domains. We provide sufficient conditions on the potential and on the drift term in order to the equation does not admit nontrivial bounded solutions. We also show that such conditions are optimal. Indeed, when they fail, the elliptic equation possesses infinitely many bounded solutions.File in questo prodotto:
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