Pointwise bounds and blow-up for Choquard–Pekar inequalities at an isolated singularity Academic Article uri icon

abstract

  • © 2016 Elsevier Inc. We study the behavior near the origin in Rn,n≥3, of nonnegative functions. u∈C2(Rn)∩Lλ(Rn) satisfying the Choquard-Pekar type inequalities. 0≤-Δu≤(|x|-α*uλ)uσ in B2(0){0} where α ∈ (0, n), λ > 0, and σ ≥ 0 are constants and * is the convolution operation in Rn. We provide optimal conditions on α, λ, and σ such that nonnegative solutions u of (0.1), (0.2) satisfy pointwise bounds near the origin.

altmetric score

  • 0.5

author list (cited authors)

  • Ghergu, M., & Taliaferro, S. D.

citation count

  • 14
  • 15

publication date

  • July 2016