Growth conditions and regularity for weak solutions to nonlinear elliptic pdes

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Abstract

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−dependence or x−independence.

Keywords

Elliptic equations
Calculus of variations
Regularity of solutions
Local Lipschitz continuity
p,qgrowth conditions
General growth conditions

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