Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

Mathematics. --- Functional analysis. --- Partial differential equations. --- Calculus of variations. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Functional Analysis. --- Differential equations, partial. --- Mathematical optimization. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Partial differential equations --- Differential equations, Partial. --- Isoperimetrical problems --- Variations, Calculus of