Boundary value problems for second-order elliptic equations Calculus of variations and optimal control; optimization Degenerate elliptic equations Differential equations, Elliptic Differential equations, Nonlinear Elliptic equations and systems Elliptic equations on manifolds, general theory Équations différentielles elliptiques Équations différentielles non linéaires Functional analysis Global analysis, analysis on manifolds Linear function spaces and their duals Manifolds Maximum principles Nonlinear eigenvalue problems, nonlinear spectral theory Nonlinear elliptic equations Partial differential equations Partial differential equations on manifolds; differential operators Qualitative properties of solutions Second-order elliptic equations Sobolev spaces and other spaces of "smooth'' functions, embedding theorems, trace theorems Spectral theory and eigenvalue problems Variational methods for second-order elliptic equations Variational problems in a geometric measure-theoretic setting