Elliptic Partial Differential Equations. Vol.1

The theory of elliptic partial differential equations develops during about two centuries together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications. It remains one of the most rapidly developing fields of mathematics. The theory of general elliptic problems is presented in the first volume of the book. A priori estimates, normal solvability and Fredholm property, index, operators with a parameter, nonlinear Fredholm operators are discussed. A particular attention is brought to elliptic problems in unbounded domains which are not yet sufficiently well presented in the existing literature and which require some special approaches. The second volume is devoted to reaction-diffusion equations. Existence and bifurcations of solutions, travelling waves, spectral properties and other questions are studied in relation with numerous applications in chemical physics, biology and medicine.