English

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

Analysis of PDEs 2019-03-13 v1

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.

Keywords

Cite

@article{arxiv.1903.04569,
  title  = {Pointwise gradient bounds for entire solutions of elliptic equations with non-standard growth conditions and general nonlinearities},
  author = {Cecilia Cavaterra and Serena Dipierro and Alberto Farina and Zu Gao and Enrico Valdinoci},
  journal= {arXiv preprint arXiv:1903.04569},
  year   = {2019}
}