Integro-Differential Elliptic Equations - Xavier Fernández-Real, Xavier Ros-Oton

Blick ins Buch

Integro-Differential Elliptic Equations (eBook)

Xavier Fernández-Real, Xavier Ros-Oton (Autoren)

eBook Download: PDF

2024
XVI, 395 Seiten
Springer Nature Switzerland (Verlag)
978-3-031-54242-8 (ISBN)

Lese- und Medienproben

Ebook-Leseprobe (PDF)

This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21^st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality.

The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries.

A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters.

Xavier Fernández-Real Girona is SNF Ambizione Fellow at EPFL. He received his PhD in Mathematics from ETH Zürich in 2020, for which he received the Dimitris N. Chorafas Prize as well as the Vicent Caselles Prize. He is the winner of the Rubio de Francia Prize from the Royal Spanish Mathematical Society and the Antonio Valle Young Researcher Award from the Spanish Society of Applied Mathematics. He is author of the book 'Regularity Theory for Elliptic PDE', jointly written with X. Ros-Oton.

Xavier Ros Oton is ICREA Research Professor at Universitat de Barcelona since 2020. Previously, he has been Assistant Professor at Universität Zürich, as well as R. H. Bing Instructor at the University of Texas at Austin. He has received several awards for young mathematicians in Spain, including the 'Premio Nacional de Investigación' for researchers under 40 in Mathematics and Computer Science. He also received the Scientific Research Award from the Fundación Princesa de Girona, as well as the Stampacchia Gold Medal. In 2022, he was elected member of the Spanish Royal Academy of Sciences.

Erscheint lt. Verlag	24.4.2024
Reihe/Serie	Progress in Mathematics
Zusatzinfo	XVI, 395 p. 22 illus., 2 illus. in color.
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	fractional Laplacian • integro-differential operators • Lévy processes • Nonlinear elliptic equations • obstacle problems
ISBN-10	3-031-54242-8 / 3031542428
ISBN-13	978-3-031-54242-8 / 9783031542428

Haben Sie eine Frage zum Produkt?

PDF (Wasserzeichen)
Größe: 11,9 MB

DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.

Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.

Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.

Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.

Print-Ausgabe

Buch | Hardcover

171,19 €