Growth conditions and regularity for weak solutions to nonlinear elliptic pdes

We describe some aspects of the process/approach to interior regularity of weak solutions to a class of nonlinear elliptic equations in divergence form, as well as of minimizers of integrals of the calculus of variations. In particular with respect to the growth conditions we emphasize some differences between solving equations and minimizing energy integrals, and also between x & minus;dependence or x & minus;independence. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

The article focuses on the interior regularity of weak solutions to a class of nonlinear elliptic equations and minimizers of integrals of the calculus of variations. It highlights differences between solving equations and minimizing energy integrals, as well as between x-dependence and x-independence.