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 SpacesMaximal monotone operatorsA theorem of Brezis-NirenbergOperator-norm convergence of the Trotter product formulaElliptic operators with infinitely many variablesPseudo-and quasiconvexities for nonsmooth functionAnisotropic surface measuresEulerian and Lagrangian variablesMultiple periodic solutions of Lagrangian systemsPorous medium equationNondiscrete Lassonde-Revalski principleGraduate 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.