This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known L8 estimates that hold for all nonlinearities. Such estimates are known to hold up to dimension 4. They are expected to be true also in dimensions 5 to 9, but this is still an open problem which has only been established in the radial case.
Cabre, X. Boundedness of stable solutions to semilinear elliptic equations: A survey. "Advanced nonlinear studies", 1 Maig 2017, vol. 17, núm. 2, p. 355-368.