Notes on the Stationary p-Laplace Equation

Notes on the Stationary p-Laplace Equation
Author: Peter Lindqvist
Publisher: Springer
Total Pages: 107
Release: 2019-04-26
Genre: Mathematics
ISBN: 3030145018

This book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based on lectures by the author that were originally delivered at the Summer School in Jyväskylä, Finland, in August 2005 and have since been updated and extended to cover various new topics, including viscosity solutions and asymptotic mean values. The p-Laplace equation is a far-reaching generalization of the ordinary Laplace equation, but it is non-linear and degenerate (p>2) or singular (p2). Thus it requires advanced methods. Many fascinating properties of the Laplace equation are, in some modified version, extended to the p-Laplace equation. Nowadays the theory is almost complete, although some challenging problems remain open./pbrp

The Laplacian on a Riemannian Manifold

The Laplacian on a Riemannian Manifold
Author: Steven Rosenberg
Publisher: Cambridge University Press
Total Pages: 190
Release: 1997-01-09
Genre: Mathematics
ISBN: 9780521468312

This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

Notes on the Infinity Laplace Equation

Notes on the Infinity Laplace Equation
Author: Peter Lindqvist
Publisher: Springer
Total Pages: 73
Release: 2016-05-25
Genre: Mathematics
ISBN: 3319315323

This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity-Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.

The obstacle problem

The obstacle problem
Author: Luis Angel Caffarelli
Publisher: Edizioni della Normale
Total Pages: 0
Release: 1999-10-01
Genre: Mathematics
ISBN: 9788876422492

The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.

Partial Differential Equations

Partial Differential Equations
Author: Walter A. Strauss
Publisher: John Wiley & Sons
Total Pages: 467
Release: 2007-12-21
Genre: Mathematics
ISBN: 0470054565

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Semilinear Elliptic Equations for Beginners

Semilinear Elliptic Equations for Beginners
Author: Marino Badiale
Publisher: Springer Science & Business Media
Total Pages: 204
Release: 2010-12-07
Genre: Mathematics
ISBN: 0857292277

Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations. This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures. Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.

Function Spaces in Analysis

Function Spaces in Analysis
Author: Krzysztof Jarosz
Publisher: American Mathematical Soc.
Total Pages: 301
Release: 2015-07-28
Genre: Education
ISBN: 1470416948

This volume contains the proceedings of the Seventh Conference on Function Spaces, which was held from May 20-24, 2014 at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

Elliptic Regularity Theory by Approximation Methods

Elliptic Regularity Theory by Approximation Methods
Author: Edgard A. Pimentel
Publisher: Cambridge University Press
Total Pages: 203
Release: 2022-09-29
Genre: Mathematics
ISBN: 1009096664

A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.