The book contains two contributions about the work of Emmanuele DiBenedetto and a selection of original papers. The authors are some of the main experts in Harnack's inequalities and nonlinear operators. These papers are part of the contributions presented during the conference to celebrate the 70th birthday of Prof. Emmanuele DiBenedetto, which was held at "Il Palazzone" in Cortona from June 18th to 24th, 2017. The papers are focused on current research topics regarding the qualitative properties of solutions, connections with calculus of variations, Harnack inequality and regularity theory. Some papers are also related to various applications. Many of the authors have shared with Prof. DiBenedetto an intense scientific and personal collaboration, while many others have taken inspiration from and further developed his field of research. The topics of the conference are certainly of great interest for the international mathematical community.

Inhalt
- What I Learnt from Emmanuele DiBenedetto. - A Short Presentation of Emmanuele's Work. - Evolutionary Problems in Non-Cylindrical Domains. - A Compactness Result for the Sobolev Embedding via Potential Theory. - Mathematical Modeling of the Rod Phototransduction Process. - Existence, Decay Time and Light Yield for a Reaction-Diffusion-Drift Equation in the Continuum Physics of Scintillators. - Boundary Harnack Type Inequality and Regularity for Quasilinear Degenerate Elliptic Equations. - Monotonicity of Positive Solutions to pu + a(u)|u|q = f (u) in the Half-Plane in the Case p 2. - Geometric Tangential Analysis and Sharp Regularity for Degenerate pdes. - Complete List of Mathematical Papers Authored by Emmanuele DiBenedetto. - Complete List ofMonographs and Textbooks Authored or Edited by Emmanuele DiBenedetto.