Stable solutions of elliptic partial differential equations. (©2011)

• Record Type: Book
• Further Information: Note: Louis Dupaigne.
• Other Names: Dupaigne, Louis
• Contents: Defining Stability; Stability and the variations of energy; Linearized stability; Elementary properties of stable solutions; Dynamical stability; Stability outside a compact set; Resolving an ambiguity The Gelfand Problem; Motivation; Dimension N = 1; Dimension N = 2; Dimension N ≥ 3; Summary Extremal Solutions; Weak solutions; Stable weak solutions; The stable branch Regularity Theory of Stable Solutions; The radial case; Back to the Gelfand problem; Dimensions N = 1, 2, 3; A geometric Poincaré formula; Dimension N = 4; Regularity of solutions of bounded Morse index Singular Stable Solutions; The Gelfand problem in the perturbed ball; Flat domains; Partial regularity of stable solutions in higher dimensions Liouville Theorems for Stable Solutions; Classifying radial stable entire solutions; Classifying stable entire solutions; Classifying solutions that are stable outside a compact set A Conjecture of E De Giorgi; Statement of the conjecture; Motivation for the conjecture; Dimension N = 2; Dimension N = 3 Further Readings; Stability versus geometry of the domain; Symmetry of stable solutions; Beyond the stable branch; The parabolic equation; Other energy functional Appendix A: Maximum Principles; Appendix B: Regularity Theory for Elliptic Operators; Appendix C: Geometric Tools References Index
• Publisher Details: Boca Raton : Taylor & Francis
• Publication Date: 2011
• Copyright Date: 2011
• Extent: 1 online resource (xiv, 317 pages), illustrations
• Subjects: 515/.3533; Differential equations, Elliptic; MATHEMATICS -- Differential Equations -- Partial; Differential equations, Elliptic; Electronic books
• Languages: English
• ISBNs: 9781420066555; 1420066552; 1420066544; 9781420066548
• Related ISBNs: 9781420066548
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.