Local Integral Estimates for Quasilinear Equations with Measure Data

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