# Liouville-type theorems for unbounded solutions of elliptic equations in half-spaces

@article{Sirakov2020LiouvilletypeTF, title={Liouville-type theorems for unbounded solutions of elliptic equations in half-spaces}, author={Boyan Sirakov and Philippe Souplet}, journal={arXiv: Analysis of PDEs}, year={2020} }

We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solutions which grow at most like the distance to the boundary to a power given by the natural scaling exponent of the equation; in other words, we rule out {\it type~I grow-up} solutions. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. Instrumental in the proof are local pointwise bounds for the logarithmic…

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