On the regularity of Anisotropic p-Laplacean Operators: the pursuit of a comprehensive theory of regularity

With this note, we aim at drawing a short, coherent, and compact guideof the state-of-the-art on the theory of basic regularity, such as local boundedness, localH ̈older continuity, Harnack estimates and some of their consequences, in the context ofsolutions to anisotropicp-Laplacean operators, elliptic and parabolic.Sunto.Con questa breve nota intendiamo proporre una panoramica, breve, coerentee concisa sullo stato dell’arte della teoria della regolarit`a degli operatorip-Laplacianianisotropici sia ellittici che parabolici. Tratteremo propriet`a di base quali la limitatezzalocale, la continuit`a H ̈olderiana, le stime di Harnack e le loro principali conseguenze.