✦ LIBER ✦

The Principal Eigenvalue and Maximum Principle for Second Order Elliptic Operators on Riemannian Manifolds

✍ Scribed by Pablo Padilla

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 221 KB
Volume: 205
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5139

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper the work of Berestycki, Nirenberg and Varadhan on the maximum principle and the principal eigenvalue for second order operators on general domains is extended to Riemannian manifolds. In particular it is proved that the refined maximum principle holds for a second order elliptic operator on a manifold if and only if the principal eigenvalue is positive.

📜 SIMILAR VOLUMES

Principal Eigenvalues and Anti – Maximum

Principal Eigenvalues and Anti – Maximum Principle for Some Quasilinear Elliptic Equations on ℝN

✍ Nikos M. Stavrakakis; Francois de Thélin 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 308 KB

A minimum principle for the principal ei

A minimum principle for the principal eigenvalue for second-order linear elliptic equations with natural boundary conditions

✍ Charles J. Holland 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 402 KB 👁 1 views

Solution of boundary and eigenvalue prob

Solution of boundary and eigenvalue problems for second-order elliptic operators in the plane using pseudoanalytic formal powers

✍ Raúl Castillo Pérez; Vladislav V. Kravchenko; Rabindranath Reséndiz Vázquez 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 262 KB

## Communicated by G. Franssens We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D = div p grad+q in the plane using pseudoanalytic function theory and in particular pseudoanalytic formal powers. Under certain conditions on the coefficients p and q w