A Note On Gradient Estimate For The Equation Associated To The P Laplace Operator
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p-Laplace Equation in the Heisenberg Group
Author | : Diego Ricciotti |
Publisher | : Springer |
Total Pages | : 96 |
Release | : 2015-12-28 |
Genre | : Mathematics |
ISBN | : 331923790X |
This works focuses on regularity theory for solutions to the p-Laplace equation in the Heisenberg group. In particular, it presents detailed proofs of smoothness for solutions to the non-degenerate equation and of Lipschitz regularity for solutions to the degenerate one. An introductory chapter presents the basic properties of the Heisenberg group, making the coverage self-contained. The setting is the first Heisenberg group, helping to keep the notation simple and allow the reader to focus on the core of the theory and techniques in the field. Further, detailed proofs make the work accessible to students at the graduate level.
Second Order Parabolic Differential Equations
Author | : Gary M. Lieberman |
Publisher | : World Scientific |
Total Pages | : 472 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 9789810228835 |
Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.
Degenerate Parabolic Equations
Author | : Emmanuele DiBenedetto |
Publisher | : Springer Science & Business Media |
Total Pages | : 402 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461208955 |
Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Notes on the P-Laplace Equation
Author | : Peter Lindqvist |
Publisher | : |
Total Pages | : 80 |
Release | : 2006 |
Genre | : Differential equations, Elliptic |
ISBN | : 9789513925864 |
Fully Nonlinear Elliptic Equations
Author | : Luis A. Caffarelli |
Publisher | : American Mathematical Soc. |
Total Pages | : 114 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 0821804375 |
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.
Theory of Sobolev Multipliers
Author | : Vladimir Maz'ya |
Publisher | : Springer Science & Business Media |
Total Pages | : 615 |
Release | : 2008-10-13 |
Genre | : Mathematics |
ISBN | : 3540694927 |
The first part of this book offers a comprehensive overview of the theory of pointwise multipliers acting in pairs of spaces of differentiable functions. The second part of the book explores several applications of this theory.
Optimization and Control for Partial Differential Equations
Author | : Roland Herzog |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 386 |
Release | : 2022-03-07 |
Genre | : Mathematics |
ISBN | : 3110696002 |
This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.
Lebesgue and Sobolev Spaces with Variable Exponents
Author | : Lars Diening |
Publisher | : Springer |
Total Pages | : 516 |
Release | : 2011-03-29 |
Genre | : Mathematics |
ISBN | : 3642183638 |
The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.