The strong maximum principle for the heat equation

Characterizing the Strong Maximum Principle

In this paper we characterize the degenerate elliptic equations F(Du) = 0 whose subsolutions (F(Du) ≥ 0) satisfy the strong maximum principle. We introduce an easily computed function f on (0,∞) which is determined by F, and we show that the strong maximum principle holds depending on whether ∫ 0+ dy f(y) is infinite or finite. This complements our previous work characterizing when the (ordinar...

The Strong Maximum Principle on Infinite Networks

We study the strong maximum principle for the heat equation associated with the Dirichlet form on an infinite network. We prove that the strong maximum principle is equivalent to the underlying graph being connected after deletion of the nodes with infinite degree. Using this result, we prove that the multiplicity of the eigenvalue 0 of a generalization of the Laplace matrix equals the number o...

Remarks on the Strong Maximum Principle for Nonlocal Operators

In this note, we study the existence of a strong maximum principle for the nonlocal operator

Extensions of the Maximum Principle: Exponential Preservation by the Heat Equation

A Maximum Principle for Periodic Solutions of the Telegraph Equation

Let L s L u be a linear differential operator acting on functions u: V a R that are defined on a fixed manifold V. These functions will belong to a Ž . certain family B ; F V, R , and the definition of B may include some boundary conditions or other requirements that must be satisfied by any function u g B. It is said that L satisfies the maximum principle if the differential inequality L u G 0...