Chapter 01- Anisotropic surface measures as limits of volume fractions.- Chapter 02- Failure of the chain rule in the non steady two-dimensional setting.- Chapter 03- On the maximality of the sum of two maximal monotone operators.- Chapter 04- Analysis and simulation of a model of phosphorus uptake by plant roots.- Chapter 05- Elliptic operators with infinitely many variables.- Chapter 06- On generalized pseudo-and quasiconvexities for nonsmooth function.- Chapter 07- On the equivalence of Eulerian and Lagrangian variables for the two-component Camassa-Holm system.- Chapter 08- Sum-intersection property of Sobolev spaces.- Chapter 09- Operator-norm convergence of the Trotter product formula on Hilbert and Banach spaces: a short survey.- Chapter 10- Multiple periodic solutions of Lagrangian systems of relativistic oscillators.- Chapter 11- Applications of a theorem of Brezis-Nirenberg.- Chapter 12- Porous medium equation with nonlocal pressure.- Chapter 13- Nondiscrete Lassonde-Revalski principle and dependent choice.

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.