Abstract
We study entire continuous viscosity solutions to fully nonlinear elliptic equations involving the conformal Hessian. We prove the strong comparison principle and Hopf Lemma for (non-uniformly) elliptic equations when one of the competitors is C1,1. We obtain as a consequence a Liouville theorem for entire solutions which are approximable by C1,1 solutions on larger and larger compact domains, and, in particular, for entire C1,1 loc solutions: they are either constants or standard bubbles.
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Li, Y., Nguyen, L., Wang, B. (2020). Towards a Liouville Theorem for Continuous Viscosity Solutions to Fully Nonlinear Elliptic Equations in Conformal Geometry. In: Chen, J., Lu, P., Lu, Z., Zhang, Z. (eds) Geometric Analysis. Progress in Mathematics, vol 333. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-34953-0_11
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DOI: https://doi.org/10.1007/978-3-030-34953-0_11
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-34952-3
Online ISBN: 978-3-030-34953-0
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