Elliptic and Parabolic Equations Involving the Hardy-Leray Potential

Ireneo Peral Alonso; Fernando Soria de Diego

Published by De Gruyter 2021

Elliptic and Parabolic Equations Involving the Hardy-Leray Potential

Ireneo Peral Alonso and Fernando Soria de Diego

Volume 38 in the series De Gruyter Series in Nonlinear Analysis and Applications

https://doi.org/10.1515/9783110606270

Overview
Contents

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

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers and graduate students in partial differential equations.
Pages
- Front matter: 20
- Main content: 494
Illustrations
- Illustrations: 6
Keywords: Hardy-Ungleichung; Nichtlineare elliptische Differentialgleichung; Nichtlineare parabolische Differentialgleichung

eBook

Published: February 22, 2021
ISBN: 9783110606270

Hardcover

Published: February 22, 2021
ISBN: 9783110603460