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

11 Mar 2019  ·  Cavaterra Cecilia, Dipierro Serena, Farina Alberto, Gao Zu, Valdinoci Enrico ·

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. read more

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Analysis of PDEs