Pointwise gradient bounds for entire solutions of elliptic equations with non-standard growth conditions and general nonlinearities

Cecilia Cavaterra , Serena Dipierro , Alberto Farina (1) , Zu Gao , Enrico Valdinoci

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We give pointwise gradient bounds for solutions of (possibly non-uniformly) elliptic partial differential equations in the entire Euclidean space. The operator taken into account is very general and comprises also the singular and degenerate nonlinear case with non-standard growth conditions. The sourcing term is also allowed to have a very general form, depending on the space variables, on the solution itself, on its gradient, and possibly on higher order derivatives if additional structural conditions are satisfied. (C) 2020 Elsevier Inc. All rights reserved.

Domaines: Mathématiques [math]

Cecilia Cavaterra, Serena Dipierro, Alberto Farina, Zu Gao, Enrico Valdinoci. Pointwise gradient bounds for entire solutions of elliptic equations with non-standard growth conditions and general nonlinearities. Journal of Differential Equations, 2021, 270, pp.435-475. ⟨10.1016/j.jde.2020.08.007⟩. ⟨hal-03621401⟩