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arXiv · 1903.04569

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

Cecilia Cavaterra·Serena Dipierro·Alberto Farina·Zu Gao·Enrico Valdinoci
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Abstract

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.

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Cecilia Cavaterra, Serena Dipierro, Alberto Farina, Zu Gao, Enrico Valdinoci. 2019-03-11. Pointwise gradient bounds for entire solutions of elliptic equations with non-standard growth conditions and general nonlinearities. https://arxiv.org/abs/1903.04569

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