Elliptic and Parabolic Equations Involving the Hardy-Leray Potential

Ireneo Peral Alonso; Fernando Soria de Diego

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Elliptic and Parabolic Equations Involving the Hardy-Leray Potential

Ireneo Peral Alonso and Fernando Soria de Diego

Language: English

Published/Copyright: 2021

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This book is in the series

Volume 38 | De Gruyter Series in Nonlinear Analysis and Applications

About this book

The scientific literature on the Hardy-Leray inequality, also known as the uncertainty principle, is very extensive and scattered. The Hardy-Leray potential shows an extreme spectral behavior and a peculiar influence on diffusion problems, both stationary and evolutionary. In this book, a big part of the scattered knowledge about these different behaviors is collected in a unified and comprehensive presentation.

An authoritative monograph on equations with the Hardy-Leray potential
Collects a large number of research results on the topic
Covers both local and nonlocal equations, and topics such as existence, uniqueness, regularity, blow-up etc.

Author / Editor information

Ireneo Peral Alonso and Fernando Soria, Universidad Autónoma de Madrid, Spain.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Contents Publicly Available Download PDF	XV
1 Motivation of the Hardy–Leray potential Requires Authentication Unlicensed Licensed	1
2 Looking at the Hardy–Leray potential Requires Authentication Unlicensed Licensed	15
3 Calderón–Zygmund theory and the Hardy–Leray potential Requires Authentication Unlicensed Licensed	29
4 Effect of the Hardy–Leray potential in the solvability of semilinear elliptic equations Requires Authentication Unlicensed Licensed	45
5 The Hardy–Leray potential in semilinear heat equations Requires Authentication Unlicensed Licensed	71
6 Elliptic equations with a nonlinearity on the gradient and the Hardy–Leray potential Requires Authentication Unlicensed Licensed	103
7 The heat equation with nonlinearity on the gradient and the Hardy–Leray potential Requires Authentication Unlicensed Licensed	137
8 Fractional Laplacian type operators Requires Authentication Unlicensed Licensed	189
9 The fractional Hardy inequality Requires Authentication Unlicensed Licensed	239
10 Calderón–Zygmund summability in the fractional setting Requires Authentication Unlicensed Licensed	263
11 Fractional semilinear elliptic problems Requires Authentication Unlicensed Licensed	305
12 The heat equation with fractional diffusion Requires Authentication Unlicensed Licensed	373
13 The influence of the Hardy potential on the linear and semilinear fractional heat equations Requires Authentication Unlicensed Licensed	433
Bibliography Requires Authentication Unlicensed Licensed	475
Alphabetical Index Requires Authentication Unlicensed Licensed	489

Publishing information

Pages and Images/Illustrations in book

eBook published on:

February 22, 2021

eBook ISBN:

9783110606270

Hardcover published on:

February 22, 2021

Hardcover ISBN:

9783110603460

Pages and Images/Illustrations in book

Front matter:

20

Main content:

494

Illustrations:

6

https://doi.org/10.1515/9783110606270

eBook ISBN: 9783110606270

Hardcover ISBN: 9783110603460

Keywords for this book

Hardy-Ungleichung; Nichtlineare elliptische Differentialgleichung; Nichtlineare parabolische Differentialgleichung

Audience(s) for this book

Researchers and graduate students in partial differential equations.

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Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Elliptic and Parabolic Equations Involving the Hardy-Leray Potential

Overview

About this book

Author / Editor information

Topics

Table of contents

Bibliographic data