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Notes On The Stationary P Laplace Equation
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Book Synopsis Notes on the Stationary p-Laplace Equation by : Peter Lindqvist
Download or read book Notes on the Stationary p-Laplace Equation written by Peter Lindqvist and published by Springer. This book was released on 2019-04-26 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Notes on the P-Laplace Equation by : Peter Lindqvist
Download or read book Notes on the P-Laplace Equation written by Peter Lindqvist and published by . This book was released on 2006 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis p-Laplace Equation in the Heisenberg Group by : Diego Ricciotti
Download or read book p-Laplace Equation in the Heisenberg Group written by Diego Ricciotti and published by Springer. This book was released on 2015-12-28 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Note on Gradient Estimate for the Equation Associated to the P-Laplace Operator by :
Download or read book A Note on Gradient Estimate for the Equation Associated to the P-Laplace Operator written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Notes on the Infinity Laplace Equation by : Peter Lindqvist
Download or read book Notes on the Infinity Laplace Equation written by Peter Lindqvist and published by Springer. This book was released on 2016-05-25 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The obstacle problem by : Luis Angel Caffarelli
Download or read book The obstacle problem written by Luis Angel Caffarelli and published by Edizioni della Normale. This book was released on 1999-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Physics and Its Interactions by : Shuji Machihara
Download or read book Mathematical Physics and Its Interactions written by Shuji Machihara and published by Springer Nature. This book was released on with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Laplacian on a Riemannian Manifold by : Steven Rosenberg
Download or read book The Laplacian on a Riemannian Manifold written by Steven Rosenberg and published by Cambridge University Press. This book was released on 1997-01-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Book Synopsis Maximal Function Methods for Sobolev Spaces by : Juha Kinnunen
Download or read book Maximal Function Methods for Sobolev Spaces written by Juha Kinnunen and published by American Mathematical Soc.. This book was released on 2021-08-02 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy's inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy's inequalities. At the end of the book, the theory of weak solutions to the p p-Laplace equation and the use of maximal function techniques is this context are discussed. The book is directed to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
Book Synopsis Handbook of Differential Equations: Stationary Partial Differential Equations by : Michel Chipot
Download or read book Handbook of Differential Equations: Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2007-05-03 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of self contained state-of-the art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching. - written by well-known experts in the field - self contained volume in series covering one of the most rapid developing topics in mathematics
Book Synopsis The Fractional Laplacian by : Wenxiong Chen
Download or read book The Fractional Laplacian written by Wenxiong Chen and published by World Scientific. This book was released on 2020-06-09 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Different from most other books, it emphasizes on illuminating the ideas behind the formal concepts and proofs, so that readers can quickly grasp the essence.
Book Synopsis Stability of Solutions of a One-dimensional P-Laplace Equation with Periodic Potential by : Matthew Lewis
Download or read book Stability of Solutions of a One-dimensional P-Laplace Equation with Periodic Potential written by Matthew Lewis and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Laplace Transforms and Fourier Series by : P.P.G. Dyke
Download or read book An Introduction to Laplace Transforms and Fourier Series written by P.P.G. Dyke and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material.
Book Synopsis Squigonometry: The Study of Imperfect Circles by : Robert D. Poodiack
Download or read book Squigonometry: The Study of Imperfect Circles written by Robert D. Poodiack and published by Springer Nature. This book was released on 2022-12-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces generalized trigonometric functions through the exploration of imperfect circles: curves defined by |x|p + |y|p = 1 where p ≥ 1. Grounded in visualization and computations, this accessible, modern perspective encompasses new and old results, casting a fresh light on duality, special functions, geometric curves, and differential equations. Projects and opportunities for research abound, as we explore how similar (or different) the trigonometric and squigonometric worlds might be. Comprised of many short chapters, the book begins with core definitions and techniques. Successive chapters cover inverse squigonometric functions, the many possible re-interpretations of π, two deeper dives into parameterizing the squigonometric functions, and integration. Applications include a celebration of Piet Hein’s work in design. From here, more technical pathways offer further exploration. Topics include infinite series; hyperbolic, exponential, and logarithmic functions; metrics and norms; and lemniscatic and elliptic functions. Illuminating illustrations accompany the text throughout, along with historical anecdotes, engaging exercises, and wry humor. Squigonometry: The Study of Imperfect Circles invites readers to extend familiar notions from trigonometry into a new setting. Ideal for an undergraduate reading course in mathematics or a senior capstone, this book offers scaffolding for active discovery. Knowledge of the trigonometric functions, single-variable calculus, and initial-value problems is assumed, while familiarity with multivariable calculus and linear algebra will allow additional insights into certain later material.
Book Synopsis Nonlinear Potential Theory of Degenerate Elliptic Equations by : Juha Heinonen
Download or read book Nonlinear Potential Theory of Degenerate Elliptic Equations written by Juha Heinonen and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
Book Synopsis Theory of Sobolev Multipliers by : Vladimir Maz'ya
Download or read book Theory of Sobolev Multipliers written by Vladimir Maz'ya and published by Springer Science & Business Media. This book was released on 2008-10-13 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Critical Points of Solutions to the P-Laplace Equation in Dimension Two by : G. Alessandrini
Download or read book Critical Points of Solutions to the P-Laplace Equation in Dimension Two written by G. Alessandrini and published by . This book was released on 1986 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
