Local and global behaviour of nonlinear equations with natural growth terms

Abstract

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.

In memory of Professor Nigel Kalton

Cited by in corpus (5)

• Nonlocal equations with measure data
• Nonlinear elliptic equations and intrinsic potentials of Wolff type
• Global estimates for kernels of Neumann series and Green's functions
• Pointwise estimates of Brezis-Kamin type for solutions of sublinear elliptic equations
• Finite energy solutions of quasilinear elliptic equations with sub-natural growth terms