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A-Harmonic Equation with Differential Forms

A-Harmonic Equation with Differential Forms PDF Author: Yuxia Tong
Publisher: LAP Lambert Academic Publishing
ISBN: 9783330323780
Category :
Languages : en
Pages : 136

Book Description
Differential forms have been widely studied and used in many fields, such as physics, general relativity, theory of elasticity, quasiconformal analysis, electromagnetism, and differential geometry, etc.. They can be used to describe various systems of partial differential equations and to express different geometrical structures on manifolds. This book was written in the light of this considerations.

A-Harmonic Equation with Differential Forms

A-Harmonic Equation with Differential Forms PDF Author: Yuxia Tong
Publisher: LAP Lambert Academic Publishing
ISBN: 9783330323780
Category :
Languages : en
Pages : 136

Book Description
Differential forms have been widely studied and used in many fields, such as physics, general relativity, theory of elasticity, quasiconformal analysis, electromagnetism, and differential geometry, etc.. They can be used to describe various systems of partial differential equations and to express different geometrical structures on manifolds. This book was written in the light of this considerations.

Inequalities for Differential Forms

Inequalities for Differential Forms PDF Author: Ravi P. Agarwal
Publisher: Springer Science & Business Media
ISBN: 0387684174
Category : Mathematics
Languages : en
Pages : 388

Book Description
This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

The Pullback Equation for Differential Forms

The Pullback Equation for Differential Forms PDF Author: Gyula Csató
Publisher: Springer Science & Business Media
ISBN: 0817683135
Category : Mathematics
Languages : en
Pages : 436

Book Description
An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map φ so that it satisfies the pullback equation: φ*(g) = f. In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 ≤ k ≤ n–1. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge–Morrey decomposition and to give several versions of the Poincaré lemma. The core of the book discusses the case k = n, and then the case 1≤ k ≤ n–1 with special attention on the case k = 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Hölder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on Hölder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation. The Pullback Equation for Differential Forms is a self-contained and concise monograph intended for both geometers and analysts. The book may serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars.

Proceedings of the Conference on Differential & Difference Equations and Applications

Proceedings of the Conference on Differential & Difference Equations and Applications PDF Author: Ravi P. Agarwal
Publisher: Hindawi Publishing Corporation
ISBN: 9789775945389
Category : Difference equations
Languages : en
Pages : 1237

Book Description


Nonlinear Analysis, Differential Equations, and Applications

Nonlinear Analysis, Differential Equations, and Applications PDF Author: Themistocles M. Rassias
Publisher: Springer Nature
ISBN: 3030725634
Category : Mathematics
Languages : en
Pages : 793

Book Description
This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics. Chapters in this volume investigate compound superquadratic functions, the Hyers–Ulam Stability of functional equations, edge degenerate pseudo-hyperbolic equations, Kirchhoff wave equation, BMO norms of operators on differential forms, equilibrium points of the perturbed R3BP, complex zeros of solutions to second order differential equations, a higher-order Ginzburg–Landau-type equation, multi-symplectic numerical schemes for differential equations, the Erdős-Rényi network model, strongly m-convex functions, higher order strongly generalized convex functions, factorization and solution of second order differential equations, generalized topologically open sets in relator spaces, graphical mean curvature flow, critical point theory in infinite dimensional spaces using the Leray-Schauder index, non-radial solutions of a supercritical equation in expanding domains, the semi-discrete method for the approximation of the solution of stochastic differential equations, homotopic metric-interval L-contractions in gauge spaces, Rhoades contractions theory, network centrality measures, the Radon transform in three space dimensions via plane integration and applications in positron emission tomography boundary perturbations on medical monitoring and imaging techniques, the KdV-B equation and biomedical applications.

Analytic Number Theory, Approximation Theory, and Special Functions

Analytic Number Theory, Approximation Theory, and Special Functions PDF Author: Gradimir V. Milovanović
Publisher: Springer
ISBN: 149390258X
Category : Mathematics
Languages : en
Pages : 880

Book Description
This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.

Frontiers in Functional Equations and Analytic Inequalities

Frontiers in Functional Equations and Analytic Inequalities PDF Author: George A. Anastassiou
Publisher: Springer Nature
ISBN: 3030289508
Category : Mathematics
Languages : en
Pages : 753

Book Description
This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.

Nonlinear Analysis

Nonlinear Analysis PDF Author: Panos M. Pardalos
Publisher: Springer Science & Business Media
ISBN: 146143498X
Category : Mathematics
Languages : en
Pages : 893

Book Description
The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

The [rho]-harmonic Equation and Recent Advances in Analysis

The [rho]-harmonic Equation and Recent Advances in Analysis PDF Author: Pietro Poggi-Corradini
Publisher: American Mathematical Soc.
ISBN: 0821836102
Category : Mathematics
Languages : en
Pages : 211

Book Description
Comprised of papers from the IIIrd Prairie Analysis Seminar held at Kansas State University, this book reflects the many directions of current research in harmonic analysis and partial differential equations. Included is the work of the distinguished main speaker, Tadeusz Iwaniec, his invited guests John Lewis and Juan Manfredi, and many other leading researchers. The main topic is the so-called p-harmonic equation, which is a family of nonlinear partial differential equations generalizing the usual Laplace equation. This study of p-harmonic equations touches upon many areas of analysis with deep relations to functional analysis, potential theory, and calculus of variations. The material is suitable for graduate students and research mathematicians interested in harmonic analysis and partial differential equations.

Optimization in Science and Engineering

Optimization in Science and Engineering PDF Author: Themistocles M. Rassias
Publisher: Springer
ISBN: 1493908081
Category : Mathematics
Languages : en
Pages : 610

Book Description
Optimization in Science and Engineering is dedicated in honor of the 60th birthday of Distinguished Professor Panos M. Pardalos. Pardalos’s past and ongoing work has made a significant impact on several theoretical and applied areas in modern optimization. As tribute to the diversity of Dr. Pardalos’s work in Optimization, this book comprises a collection of contributions from experts in various fields of this rich and diverse area of science. Topics highlight recent developments and include: Deterministic global optimization Variational inequalities and equilibrium problems Approximation and complexity in numerical optimization Non-smooth optimization Statistical models and data mining Applications of optimization in medicine, energy systems, and complex network analysis This volume will be of great interest to graduate students, researchers, and practitioners, in the fields of optimization and engineering.