Local Integral Estimates for Quasilinear Equations with Measure Data

Abstract EN

Local integral estimates as well as local nonexistence results for a class of quasilinear equations - Δ p u = σ P ( u ) + ω for p > 1 and Hessian equations F k - u = σ P ( 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 α u β with α > 0 and β ≥ 1 or P ( u ) = u p - 1 .