From Ordinary to Partial Differential Equations

Prof. Giampiero Esposito (1962) obtained an honours (cum laude) degree in Physics from Naples University in 1986, and was a St. John's Benefactor's Scholar at DAMTP in Cambridge (UK) from 1987 to 1991, where he received the  J.T. Knight Prize Essay award in 1989 and obtained his Ph.D. degree. He was elected to INFN and ICTP post-doctoral positions at Naples and Trieste, respectively, and has been an INFN Research Fellow at Naples (position with tenure) since 1993, and INFN Primo Ricercatore since 2007.His original contributions are mainly devoted to quantum gravity and quantum field theory on manifolds with boundary (one-loop conformal anomalies, mixed and diff-invariant boundary conditions for Euclidean quantum gravity, heat-kernel asymptotics, Casimir effect and measurement of variations of zero-point energy), spontaneous symmetry breaking in the early universe, accelerated expansion of the universe, singularity avoidance in quantum cosmology, and scattering fromsingular potentials in quantum mechanics.

“The selection of material is quite interesting and the book could be useful for graduate students and specialists conducting research in related areas.” (Svitlana P. Rogovchenko, zbMath 1419.00002, 2019)“This is a comprehensive textbook, making it well suited for beginner to intermediate graduate-level courses in partial differential equations. … This book would benefit from the addition of exercise problems, but this fact does not detract from its many merits. In the end, this text is well organized and offers a clear conceptual framework to approach proofs. Summing Up: Recommended. Graduate students, researchers,and faculty.” (V. K. Chellamuthu, Choice, Vol. 55 (9), May, 2018)

• 1 Ordinary differential equations.- 2 Linear elliptic equations.- 3  Calculus of variations.- 4 Linear and non-linear hyperbolic equations.- 5 Parabolic equations.- 6 Fuchsian functions.- 7 The Riemann –function.- 8 A window on modern theory.- 9 References.