The Scientific World Journal (Jan 2016)

Local Integral Estimates for Quasilinear Equations with Measure Data

  • Qiaoyu Tian,
  • Shengzhi Zhang,
  • Yonglin Xu,
  • Jia Mu

DOI
https://doi.org/10.1155/2016/5742063
Journal volume & issue
Vol. 2016

Abstract

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Local integral estimates as well as local nonexistence results for a class of quasilinear equations -Δpu=σP(u)+ω for p>1 and Hessian equations Fk-u=σP(u)+ω were established, where σ is a nonnegative locally integrable function or, more generally, a locally finite measure, ω is a positive Radon measure, and P(u)~exp⁡αuβ with α>0 and β≥1 or P(u)=up-1.