Comparison Principles for General Potential Theories and PDEs
eBook - PDF

Comparison Principles for General Potential Theories and PDEs

  1. 225 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Comparison Principles for General Potential Theories and PDEs

About this book

An examination of the symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories

In recent years, there has evolved a symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories. This book examines important aspects of this story. One main purpose is to prove comparison principles for nonlinear potential theories in Euclidian spaces straightforwardly from duality and monotonicity under the weakest possible notion of ellipticity. The book also shows how to deduce comparison principles for nonlinear differential operators, by marrying these two points of view, under the correspondence principle.

The authors explain that comparison principles are fundamental in both contexts, since they imply uniqueness for the Dirichlet problem. When combined with appropriate boundary geometries, yielding suitable barrier functions, they also give existence by Perron's method. There are many opportunities for cross-fertilization and synergy. In potential theory, one is given a constraint set of 2-jets that determines its subharmonic functions. The constraint set also determines a family of compatible differential operators. Because there are many such operators, potential theory strengthens and simplifies the operator theory. Conversely, the set of operators associated with the constraint can influence the potential theory.

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Information

Publisher
Princeton University Press
Year
2023
Print ISBN
9780691243627
9780691243610
eBook ISBN
9780691243641
Topic
Mathematics
Subtopic
Differential Equations
Index
Mathematics

Table of contents

  1. Cover
  2. Contents
  3. Preface
  4. Guide for the Reader
  5. I. A Comprehensive Introduction
  6. II. The Potential Theory Approach
  7. III. Marrying Potential Theory to Operator Theory via the Correspondence Principle
  8. IV. Applications to PDEs
  9. Appendix
  10. Bibliography
  11. Index

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Yes, you can access Comparison Principles for General Potential Theories and PDEs by Marco Cirant,F. Reese Harvey,H. Blaine Lawson,Kevin R. Payne in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over 1.5 million books available in our catalogue for you to explore.