Local Integral Estimates for Quasilinear Equations with Measure Data

Abstract

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.