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

Intro -- Thanks -- Preface -- A tribute to Patrizia Pucci -- 1. Introduction -- 2. The early years and Lamberto Cesari's influence (1976-1986) -- 3. The exemplary collaboration with James Serrin (1984-2011) -- 4. A leading mathematical force in Perugia -- 5. A (temporary) conclusion -- A scientific profile of Patrizia Pucci -- References -- Monographs, published books and handouts -- The Liouville theorem for homogeneous elliptic differential inequalities -- conm11880.start.0 -- Multiplicity results for porous media and fast diffusion equations with a quadratic gradient term -- 1. Introduction -- 2. Some results for an elliptic-parabolic problem with measure data -- 3. Some results for an elliptic-parabolic problem with singular measure data -- 4. The Porous medium problem with quadratic gradient term: A multiplicity result -- Acknowledgement -- References -- A priori estimates for solutions of -Kirchhoff systems under dynamic boundary conditions -- 1. Introduction -- 2. Preliminaries -- 3. Lifespan estimates for (1.1) -- Acknowledgments -- References -- Higher order linear parabolic equations -- 1. Introduction -- 2. Heat kernel estimates -- 3. The Fokker-Planck equation -- 4. Asymptotic behavior of the solution -- 5. Positivity preserving property -- References -- Sources of Nonlinearity in the Kinetic Theory for Active Particles with Focus on the Formation of Political Opinions -- 1. On the hallmarks of the kinetic theory for active particles and plan of the paper -- 2. Mathematical structures -- 3. Sources of Nonlinearities -- 4. Opinion Formation in a Political Competition -- 5. Critical analysis -- References -- Yamabe type equations with sign-changing nonlinearities on the Heisenberg group, and the role of Green functions -- 1. Introduction -- 2. Proof of Theorem 1 -- 3. Another proof of Theorem 1 and a general result -- References.

Asymptotic behavior of the solution to variational inequalities with joint constraints on its value and its gradient -- 1. Introduction -- 2. A Model Problem -- 3. The General Case -- Acknowledgments -- References -- Existence and uniqueness of solutions to a Cauchy problem modeling the dynamics of socio-political conflicts -- 1. Introduction -- 2. The mathematical model and the initial value problem -- 3. Solution to the initial value problem -- Acknowledgement -- References -- Regularity points of -homeomorphisms in the plane -- 1. Introduction -- 2. Preliminary results -- 3. The bi-ACL mappings -- 4. Proof of Theorem 1.2 -- 5. Proof of Theorem 1.1 -- References -- Energy Estimates and Integral Harnack inequality for some doubly nonlinear singular parabolic equations -- 1. Introduction -- 2. Weak solutions and energy estimates -- 3. A DeGiorgi-type lemma -- 4. A variant of DeGiorgi-type lemma -- 5. A ¹_{ }-form of the Harnack Inequality for 2&lt -- + &lt -- 3 -- References -- Initial value problems for diffusion equations with singular potential -- 1. Introduction -- 2. The subcritical case -- 3. The supercritical case -- 4. Initial trace -- 5. Appendix: the case of a bounded domain -- References -- On a class of fully nonlinear PDEs from complex geometry -- 1. Pseudoconvexity and Levi curvature -- 2. The Levi curvature equation -- 3. The sub-Riemannian structure of the Levi curvature operator -- 4. The Levi curvature in high dimension -- 5. The Levi curvature operators -- 6. Spherical symmetry results -- 7. The Dirichlet problem: viscosity and classical solutions -- References -- Concentration of conformal volume, improved Moser-Trudinger inequalities and Toda systems -- 1. Introduction -- Acknowledgements -- 2. Proof of Theorem 1.2 -- 3. Proof of Theorem 1.3 -- References.

Periodic solutions of Lagrangian difference systems: Periodic nonlinearities (almost) don't matter -- 1. Introduction -- 2. Notations, norms, identities -- 3. The case of the -Laplacian -- 4. The case of the curvature operator -- 5. The case of the relativistic operator -- References -- A limit problem for degenerate quasilinear variational inequalities in cylinders -- 1. Introduction and main results -- 2. Proofs of the Lemmas -- 3. Proof of the Theorem -- References -- Strong solutions for the wave equation with a kinetic boundary condition -- 1. Introduction and main result -- 2. Preliminaries and functional setting -- 3. Elliptic theory -- 4. Proof of Theorem 1 -- References.

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