The book collects the most significant contributions of the outstanding Czech mathematician Jindich Neas, who was honoured with the Order of Merit of the Czech Republic by President Václav Havel. Starting with Neas's brief biography and short comments on his role in the beginnings of modern PDE research in Prague, the book then follows the periods of his research career. The first part is devoted to the linear theory of partial differential equations. Its topics include the variational approach to linear boundary value problems and the Rellich - Neas inequalities, together with their applications to boundary regularity. The second part is concerned with the regularity for nonlinear elliptic systems, which are related to Hilbert's 19th and 20th problems. The third part focuses on Nonlinear Functional Analysis and its applications to non-linear PDEs, while the last part deals with topics in the mathematical theory of various models in Continuum Mechanics, including elasticity and plasticity, the Navier-Stokes equations, transonic flows, and multipolar fluids.

The editorial contributions were written by: I. Babuka, P. Ciarlet, P. Drábek, M. Feistauer, I. Hlaváek, J. Jaruek, O. John, J. Kristensen, A. Kufner, J. Málek, G. Mingione, . Neasová, M. Pokorný, P. Quittner, T. Roubíek, G. Seregin and J. Stará.

First time that J. Necas' important results have been collected in one publication Some of the articles are not anymore available elsewhere The theory of the PDEs of continuum mechanics is perhaps even more popular today than it was when Necas's seminal contributions to this area were written

Inhalt
1 Introduction.- 2 Short Biography of J. Neas.- 3 Complete List of Neas' works.- 4 J. Neas in the early 1960s.- 5 J. Neas and the Prague School of PDE.- 6 Linear Elliptic Operators.- 7.1 Regularity for Non-linear Equations and Systems.- 7.2 Contribution of Mingione and Kristensen.- 8. Non-linear Functional Analysis, Calculus of Variations.- 9. Solid Mechanics, Elasticity, Thermoelasticity, and Plasticity.- 9.1 Mechanics of Solids.- 9.2 The Contribution of Jindich Neas to the Development of the Theory of Solvability of Contact Problems.- 10 Fluid Mechanics.- 11 Comments and Recollections by Collaborators and Students.- 12 Some Notable Personal Correspondence.- 13 Photographs.