Stratified Lie Groups and Potential Theory for Their Sub-Laplacians

Stratified Lie Groups and Potential Theory for Their Sub-Laplacians PDF

Author: Andrea Bonfiglioli

Publisher: Springer Science & Business Media

Published: 2007-08-24

Total Pages: 812

ISBN-13: 3540718974

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This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.

Analysis and Partial Differential Equations: Perspectives from Developing Countries

Analysis and Partial Differential Equations: Perspectives from Developing Countries PDF

Author: Julio Delgado

Publisher: Springer

Published: 2019-01-27

Total Pages: 269

ISBN-13: 3030056570

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This volume presents current trends in analysis and partial differential equations from researchers in developing countries. The fruit of the project 'Analysis in Developing Countries', whose aim was to bring together researchers from around the world, the volume also includes some contributions from researchers from developed countries. Focusing on topics in analysis related to partial differential equations, this volume contains selected contributions from the activities of the project at Imperial College London, namely the conference on Analysis and Partial Differential Equations held in September 2016 and the subsequent Official Development Assistance Week held in November 2016. Topics represented include Fourier analysis, pseudo-differential operators, integral equations, as well as related topics from numerical analysis and bifurcation theory, and the countries represented range from Burkina Faso and Ghana to Armenia, Kyrgyzstan and Tajikistan, including contributions from Brazil, Colombia and Cuba, as well as India and China. Suitable for postgraduate students and beyond, this volume offers the reader a broader, global perspective of contemporary research in analysis.

Geometric Control Theory and Sub-Riemannian Geometry

Geometric Control Theory and Sub-Riemannian Geometry PDF

Author: Gianna Stefani

Publisher: Springer

Published: 2014-06-05

Total Pages: 385

ISBN-13: 331902132X

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Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.

Modern Problems in PDEs and Applications

Modern Problems in PDEs and Applications PDF

Author: Marianna Chatzakou

Publisher: Springer Nature

Published: 2024

Total Pages: 187

ISBN-13: 3031567323

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The principal aim of the volume is gathering all the contributions given by the speakers (mini courses) and some of the participants (short talks) of the summer school "Modern Problems in PDEs and Applications" held at the Ghent Analysis and PDE Center from 23 August to 2 September 2023. The school was devoted to the study of new techniques and approaches for solving partial differential equations, which can either be considered or arise from the physical point of view or the mathematical perspective. Both sides are extremely important since theories and methods can be developed independently, aiming to gather each other in a common objective. The aim of the summer school was to progress and advance in the problems considered. Note that real-world problems and their applications are classical study trends in physical or mathematical modelling. The summer school was organised in a friendly atmosphere and synergy, and it was an excellent opportunity to promote and encourage the development of the subject in the community.

Quantization on Nilpotent Lie Groups

Quantization on Nilpotent Lie Groups PDF

Author: Veronique Fischer

Publisher: Birkhäuser

Published: 2016-03-08

Total Pages: 568

ISBN-13: 3319295586

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This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups, nilpotent Lie groups, and the analysis of Rockland operators on graded Lie groups together with their associated Sobolev spaces. For the specific example of the Heisenberg group the theory is illustrated in detail. In addition, the book features a brief account of the corresponding quantization theory in the setting of compact Lie groups. The monograph is the winner of the 2014 Ferran Sunyer i Balaguer Prize.

Harmonic Analysis and Partial Differential Equations

Harmonic Analysis and Partial Differential Equations PDF

Author: Michael Ruzhansky

Publisher: Springer Nature

Published: 2023-03-06

Total Pages: 241

ISBN-13: 3031243110

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This book collects papers related to the session “Harmonic Analysis and Partial Differential Equations” held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.

Geometric Methods in PDE’s

Geometric Methods in PDE’s PDF

Author: Giovanna Citti

Publisher: Springer

Published: 2015-10-31

Total Pages: 381

ISBN-13: 3319026666

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The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.

p-Laplace Equation in the Heisenberg Group

p-Laplace Equation in the Heisenberg Group PDF

Author: Diego Ricciotti

Publisher: Springer

Published: 2015-12-28

Total Pages: 96

ISBN-13: 331923790X

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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.

The Higher Infinite

The Higher Infinite PDF

Author: Akihiro Kanamori

Publisher: Springer Science & Business Media

Published: 2008-11-23

Total Pages: 555

ISBN-13: 3540888675

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Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.

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