Geometric Analysis of Quasilinear Inequalities on Complete Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Analysis of Quasilinear Inequalities on Complete Manifolds write by Bruno Bianchini. This book was released on 2021-01-18. Geometric Analysis of Quasilinear Inequalities on Complete Manifolds available in PDF, EPUB and Kindle. This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs
Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs write by Emanuel Indrei. This book was released on 2023-01-09. Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs available in PDF, EPUB and Kindle. This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.
The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems
The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems write by Olivier Druet. This book was released on 2002. The $AB$ Program in Geometric Analysis: Sharp Sobolev Inequalities and Related Problems available in PDF, EPUB and Kindle. Function theory and Sobolev inequalities have been the target of investigation for many years. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The $AB$ programme is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. This text summarizes the results of contemporary research and gives an up-to-date report on the field.
Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs
Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs write by Alexander Grigor'yan. This book was released on 2021-01-18. Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs available in PDF, EPUB and Kindle. The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities
Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities write by Emmanuel Hebey. This book was released on 2000-10-27. Nonlinear Analysis on Manifolds: Sobolev Spaces and Inequalities available in PDF, EPUB and Kindle. This volume offers an expanded version of lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. ``Several surprising phenomena appear when studying Sobolev spaces on manifolds,'' according to the author. ``Questions that are elementary for Euclidean space become challenging and give rise to sophisticated mathematics, where the geometry of the manifold plays a central role.'' The volume is organized into nine chapters. Chapter 1 offers a brief introduction to differential and Riemannian geometry. Chapter 2 deals with the general theory of Sobolev spaces for compact manifolds. Chapter 3 presents the general theory of Sobolev spaces for complete, noncompact manifolds. Best constants problems for compact manifolds are discussed in Chapters 4 and 5. Chapter 6 presents special types of Sobolev inequalities under constraints. Best constants problems for complete noncompact manifolds are discussed in Chapter 7. Chapter 8 deals with Euclidean-type Sobolev inequalities. And Chapter 9 discusses the influence of symmetries on Sobolev embeddings. An appendix offers brief notes on the case of manifolds with boundaries. This topic is a field undergoing great development at this time. However, several important questions remain open. So a substantial part of the book is devoted to the concept of best constants, which appeared to be crucial for solving limiting cases of some classes of PDEs. The volume is highly self-contained. No familiarity is assumed with differentiable manifolds and Riemannian geometry, making the book accessible to a broad audience of readers, including graduate students and researchers.
