Integro-Differential Elliptic Equations

Fernández-Real, Xavier, Ros-Oton, Xavier

Integro-Differential Elliptic Equations
  • 出版商: Birkhauser Boston
  • 出版日期: 2024-04-25
  • 售價: $6,940
  • 貴賓價: 9.5 折 $6,593
  • 語言: 英文
  • 頁數: 395
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 303154241X
  • ISBN-13: 9783031542411

    • 下單後立即進貨 (約1週~2週)

商品描述

This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st 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.

商品描述(中文翻譯)

這本專著提供了一個自成一體的介紹，關於在21世紀主要發展的積分-微分橢圓方程的正則性理論。這類方程在分析學、概率論、數學物理以及應用科學的多個領域中都具有重要意義。本書詳細介紹了所有必要的技巧，主要關注主要思想，而不是證明所有結果的最大一般性。
首先介紹了基本的構建模塊，包括對拉普拉斯算子的平方根和線性方程的弱解的研究。隨後，發展了非線性方程的黏滯解理論，並提供了在這個背景下的主要已知結果的證明。分析以對積分-微分算子的障礙問題的研究結束，並確定了解的正則性和自由邊界。
這本書的一個獨特特點在於，幾乎所有涵蓋的材料都是首次以專著形式呈現的，並且幾個證明簡化了原始論文中的證明。此外，各章節中列出了各種未解決的問題。

作者簡介

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.

作者簡介(中文翻譯)

Xavier Fernández-Real Girona是EPFL的SNF Ambizione Fellow。他於2020年從ETH Zürich獲得數學博士學位，並因此獲得了Dimitris N. Chorafas獎和Vicent Caselles獎。他是西班牙皇家數學學會的Rubio de Francia獎和西班牙應用數學學會的Antonio Valle青年研究者獎的獲獎者。他與X. Ros-Oton合著了《橢圓型偏微分方程的正則性理論》一書的作者。

Xavier Ros Oton自2020年起擔任巴塞隆納大學的ICREA研究教授。此前，他曾在蘇黎世大學擔任助理教授，並在德克薩斯大學奧斯汀分校擔任R. H. Bing講師。他曾獲得多個西班牙年輕數學家獎，包括數學和計算機科學領域40歲以下研究人員的“國家研究獎”。他還獲得了Fundación Princesa de Girona的科學研究獎和Stampacchia金牌。2022年，他當選為西班牙皇家科學院院士。

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