Solvability Regularity and Optimal Control of Boundary Value Problems for PDEs : In Honour of Prof. Gianni Gilardi 1 Rate of convergence for eigenfunctions of Aharonov Bohm operators with a moving pole 2 Nondecreasing solutions to doubly nonlinear equations 3 Identification problems for degenerate integro differential equations 4 A phase transition model describing auxetic materials 5 Global well posedness for a phase transition model with irreversible evolution and acceleration forces 6 Perimeter symmetrization of some dynamic and stationary equations involving the Monge Ampere operator 7 Optimal boundary control of a nonstandard Cahn Hilliard system with dynamic boundary condition and double obstacle inclusions 8 Nontrivial solutions of quasilinear elliptic equatons with natural growth term 9 On a diffuse interface model for tumour growth with non local interactions and degenerate mobilities 10 A boundary control problem for the equation and dynamic boundary condition of Cahn Hilliard type 11 New class of doubly nonlinear evolution equations governed by time dependent subdifferentials 12 Boundedness of solutions to a degenerate diffusion equation 13 Optimal a priori error estimates of parabolic optimal control problems with a moving point control 14 A note on the feedback stabilization of a Cahn Hilliard type system with a singular logarithmic potential 15 Mathematical analysis of a parabolic elliptic model for brain lactate kinetics 16 Weak formulation for singular diffusion equation with dynamic boundary condition 17 Smooth and broken minimizers of some free discontinuity problems 18 Stability results for abstract evolution equations with intermittent time delay feedback 19 From visco energetic to energetic and balanced viscosity solutions of rate independent systems 20 A duality approach in some boundary value problems 21 On the structural properties of nonlinear flows This volume gathers contributions in the field of partial differential equations with a focus on mathematical models in phase transitions complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self contained manner and describe new achievements and or the state of the art in their line of research providing interested readers with an overview of recent advances and future research directions in PDEs