**Contemporary Mathematics**

Volume: 594;
2013;
307 pp;
Softcover

MSC: Primary 35;
Secondary 34; 47; 58

Print ISBN: 978-0-8218-8736-3

Product Code: CONM/594

List Price: $111.00

Individual Member Price: $88.80

**Electronic ISBN: 978-1-4704-0992-0
Product Code: CONM/594.E**

List Price: $111.00

Individual Member Price: $88.80

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# Recent Trends in Nonlinear Partial Differential Equations I: Evolution Problems

Share this page *Edited by *
*James B. Serrin; Enzo L. Mitidieri; Vicenţiu D. Rădulescu*

This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28–June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday.

The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide ranging influence of Professor Pucci on the field of nonlinear analysis and partial differential equations.

In her own work, Patrizia Pucci has been a seminal influence in many important areas: the maximum principle, qualitative analysis of solutions to many classes of nonlinear PDEs (Kirchhoff problems, polyharmonic systems), mountain pass theorem in the critical case, critical exponents, variational identities, as well as various degenerate or singular phenomena in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.

The companion volume (Contemporary Mathematics, Volume 595) is devoted to stationary problems in nonlinear partial differential equations.

#### Table of Contents

# Table of Contents

## Recent Trends in Nonlinear Partial Differential Equations I: Evolution Problems

- Thanks vii8 free
- Preface ix10 free
- A tribute to Patrizia Pucci 112 free
- A scientific profile of Patrizia Pucci 920
- The Liouville theorem for homogeneous elliptic differential inequalities 1930
- conm11880.start.0 2132
- Multiplicity results for porous media and fast diffusion equations with a quadratic gradient term 3748
- A priori estimates for solutions of 𝑝–Kirchhoff systems under dynamic boundary conditions 5970
- Higher order linear parabolic equations 7788
- Sources of Nonlinearity in the Kinetic Theory for Active Particles with Focus on the Formation of Political Opinions 99110
- Yamabe type equations with sign-changing nonlinearities on the Heisenberg group, and the role of Green functions 115126
- Asymptotic behavior of the solution to variational inequalities with joint constraints on its value and its gradient 137148
- Existence and uniqueness of solutions to a Cauchy problem modeling the dynamics of socio-political conflicts 155166
- Regularity points of 𝐴𝐶𝐿–homeomorphisms in the plane 167178
- Energy Estimates and Integral Harnack inequality for some doubly nonlinear singular parabolic equations 179190
- Initial value problems for diffusion equations with singular potential 201212
- On a class of fully nonlinear PDEs from complex geometry 231242
- 1. Pseudoconvexity and Levi curvature 231242
- 2. The Levi curvature equation 234245
- 3. The sub-Riemannian structure of the Levi curvature operator 235246
- 4. The Levi curvature in high dimension 237248
- 5. The Levi curvature operators 238249
- 6. Spherical symmetry results 239250
- 7. The Dirichlet problem: viscosity and classical solutions 240251
- References 241252

- Concentration of conformal volume, improved Moser-Trudinger inequalities and Toda systems 243254
- Periodic solutions of Lagrangian difference systems: Periodic nonlinearities (almost) don’t matter 265276
- A limit problem for degenerate quasilinear variational inequalities in cylinders 281292
- Strong solutions for the wave equation with a kinetic boundary condition 295306

#### Readership

Graduate students and research mathematicians interested in nonlinear partial differential equations.