The regularity and stability of solutions to semilinear fourth-order elliptic problems with negative exponents

@inproceedings{Lai2016TheRA,
  title={The regularity and stability of solutions to semilinear fourth-order elliptic problems with negative exponents},
  author={Baishun Lai},
  year={2016}
}
We examine the regularity of the extremal solution of the nonlinear eigenvalue problem on a general bounded domain Ω in ℝ N , with Navier boundary condition u = Δ u on ∂Ω. Firstly, we prove the extremal solution is smooth for any p > 1 and N ⩽ 4, which improves the result of Guo and Wei ( Discrete Contin. Dynam. Syst. A 34 (2014), 2561–2580). Secondly, if p = 3, N = 3, we prove that any radial weak solution of this nonlinear eigenvalue problem is smooth in the case Ω = 𝔹, which completes the… CONTINUE READING