Current research and applications in nonlinear analysis influenced by Haim Brezis and Louis Nirenberg are presented in this book by leading mathematicians. Each contribution aims to broaden reader's understanding of theories, methods, and techniques utilized to solve significant problems.

Topics include:

Sobolev Spaces

Maximal monotone operators

A theorem of Brezis-Nirenberg

Operator-norm convergence of the Trotter product formula

Elliptic operators with infinitely many variables

Pseudo-and quasiconvexities for nonsmooth function

Anisotropic surface measures

Eulerian and Lagrangian variables

Multiple periodic solutions of Lagrangian systems

Porous medium equation

Nondiscrete Lassonde-Revalski principle

Graduate students and researchers in mathematics, physics, engineering, and economics will find this book a useful reference for new techniques and research areas. Haim Brezis and Louis Nirenberg's fundamental research in nonlinear functional analysis and nonlinear partial differential equations along with their years of teaching and training students have had a notable impact in the field.