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

2019/03/11 by Cecilia Cavaterra, Cavaterra, Cecilia, Serena Dipierro +7
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1903.04569

arxiv created 2019/03/11 · arxiv updated 2019/03/13

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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