Abstract
In this paper we study the Dirichlet problem
, where σ and ω are nonnegative Borel measures, and \({\Delta_p{u} = \nabla \cdot (\nabla{u} \, |\nabla{u}|^{p-2})}\) is the p-Laplacian. Here \({\Omega \subseteq \mathbf{R}^n}\) is either a bounded domain, or the entire space. Our main estimates concern optimal pointwise bounds of solutions in terms of two local Wolff’s potentials, under minimal regularity assumed on σ and ω. In addition, analogous results for equations modeled by the k-Hessian in place of the p-Laplacian will be discussed.
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Communicated by G. Dal Maso
In memory of Professor Nigel Kalton
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Jaye, B.J., Verbitsky, I.E. Local and Global Behaviour of Solutions to Nonlinear Equations with Natural Growth Terms. Arch Rational Mech Anal 204, 627–681 (2012). https://doi.org/10.1007/s00205-011-0491-2
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DOI: https://doi.org/10.1007/s00205-011-0491-2