Current Research in Nonlinear Analysis

✍ Scribed by Themistocles M. Rassias

• Publisher: Springer International Publishing
• Year: 2018
• Tongue: English
• Leaves: 363
• Series: Springer Optimization and Its Applications 135
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-x
Anisotropic Surface Measures as Limits of Volume Fractions (Luigi Ambrosio, Giovanni E. Comi)....Pages 1-32
Failure of the Chain Rule in the Non Steady Two-Dimensional Setting (Stefano Bianchini, Paolo Bonicatto)....Pages 33-60
On the Maximality of the Sum of Two Maximal Monotone Operators (Yuqing Chen, Yeol Je Cho, Themistocles M. Rassias)....Pages 61-83
Analysis and Simulation of a Model of Phosphorus Uptake by Plant Roots (Myriam Comte)....Pages 85-97
Elliptic Operators with Infinitely Many Variables (Giuseppe Da Prato)....Pages 99-127
On Generalized Pseudo- and Quasiconvexities for Nonsmooth Functions (Ville-Pekka Eronen, Marko M. Mäkelä, Napsu Karmitsa)....Pages 129-155
On the Equivalence of Eulerian and Lagrangian Variables for the Two-Component Camassa–Holm System (Markus Grasmair, Katrin Grunert, Helge Holden)....Pages 157-201
Sum-Intersection Property of Sobolev Spaces (Petru Mironescu)....Pages 203-228
Operator-Norm Convergence of the Trotter Product Formula on Hilbert and Banach Spaces: A Short Survey (Hagen Neidhardt, Artur Stephan, Valentin A. Zagrebnov)....Pages 229-247
Multiple Periodic Solutions of Lagrangian Systems of Relativistic Oscillators (Biagio Ricceri)....Pages 249-258
Applications of a Theorem of Brezis-Nirenberg (Martin Schechter)....Pages 259-276
Porous Medium Equation with Nonlocal Pressure (Diana Stan, Félix del Teso, Juan Luis Vázquez)....Pages 277-308
Nondiscrete Lassonde-Revalski Principle and Dependent Choice (Mihai Turinici)....Pages 309-360

✦ Subjects

Mathematics; Calculus of Variations and Optimal Control; Optimization; Numerical Analysis; Functions of a Complex Variable; Real Functions; Partial Differential Equations