Dipierro S., Valdinoci E. Elliptic Partial Differential Equations from an Elementary Viewpoint: A Fresh Glance at the Classical Theory

Singapore: World Scientific Publishing Company, 2024. - 669 p. - ISBN 9811291624.This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course. The book considers many important issues such as existence, regularity, qualitative properties, and all the classical topics useful in the wide world of partial differential equations. It also includes applications with interesting examples. The structure of the book is flexible enough to allow different chapters to be taught independently. The book is friendly, welcoming, and written for a newcomer to the subject. It is essentially self-contained, making it easy to read, and all the concepts are fully explained from scratch, combining intuition and rigor, and therefore it can also be read independently by students, with limited or no supervision.
Readership: Undergraduate and graduate students in applied mathematics courses, lecturers and researchers.Preface.
About the Authors.
Acknowledgments.
What Is the Laplacian?
The Laplace Operator and Harmonic Functions.
Upper Semicontinuity and Subharmonicity.
Equations in Nondivergence Form: 𝐶 2, 𝛼 - Regularity Theory.
Equations in Nondivergence Form: 𝑊 2, 𝑝 - Regularity Theory.
The Dirichlet Problem in the Light of Capacity Theory.
Some Interesting Problems Arising from the Poisson Equation.
The Moving Plane Method.
Local Existence Theory in the Real Analytic Setting.
Appendix A An Interesting Example.
Appendix B An Application to Physical Geodesy.
References.
Index.True PDF