Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume was initiated at the Delft conference on the occasion of the retirement of Philippe Clément. It will be of interest to researchers in PDEs and functional analysis.

"Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume was initiated at the Delft conference on the occasion of the retirement of Philippe Clément. It will be of interest to researchers in PDEs and functional analysis. TOC:Preface.- Curriculum Vitae of Philippe Clément.- Contributions by G. Caristi, C. Carstensen, S. Cerrai, G. Da Prato, A.F.M. ter Elst, O. van Gaans, M. Geissert, H. Heck, M. Hieber, F. den Hollander, T.P. Hytönen, S.-O. Londen, A. Lunardi, E. Mitidieri, N. Okazawa, J. Prüss, J. Rappaz, D.W. Robinson, A. Sikora, G. Simonett, E.G.F. Thomas, L. Weis, M. Wilke, Y. Zhu."

Harnack Inequality and Applications to Solutions of Biharmonic Equations.- Clément Interpolation and Its Role in Adaptive Finite Element Error Control.- Ergodic Properties of Reaction-diffusion Equations Perturbed by a Degenerate Multiplicative Noise.- Kolmogorov Operators of Hamiltonian Systems Perturbed by Noise.- Dirichlet Forms and Degenerate Elliptic Operators.- On R-boundedness of Unions of Sets of Operators.- On the Equation div u = g and Bogovskii's Operator in Sobolev Spaces of Negative Order.- Renormalization of Interacting Diffusions: A Program and Four Examples.- Reduced Mihlin-Lizorkin Multiplier Theorem in Vector-valued L p Spaces.- Interpolation Spaces for Initial Values of Abstract Fractional Differential Equations.- Semilinear Elliptic Problems Associated with the Complex Ginzburg-Landau Equation.- Operator-valued Symbols for Elliptic and Parabolic Problems on Wedges.- Maximal L p-regularity and Long-time Behaviour of the Non-isothermal Cahn-Hilliard Equation with Dynamic Boundary Conditions.- Numerical Approximation of PDEs and Clément's Interpolation.- On Prohorov's Criterion for Projective Limits.- The H ?Holomorphic Functional Calculus for Sectorial Operators - a Survey.