A Comparison Theorem for Elliptic Differential Equations

On a Comparison Theorem for Self-adjoint Partial Differential Equations of Elliptic Type

A Liouville Theorem for Non Local Elliptic Equations

We prove a Liouville-type theorem for bounded stable solutions v ∈ C(R) of elliptic equations of the type (−∆)v = f(v) in R, where s ∈ (0, 1) and f is any nonnegative function. The operator (−∆) stands for the fractional Laplacian, a pseudo-differential operator of symbol |ξ|.

A Qualitative Phragmèn-Lindelöf Theorem for Fully Nonlinear Elliptic Equations

We establish qualitative results of Phragmèn-Lindelöf type for upper semicontinuous viscosity solutions of fully nonlinear partial differential inequalities of the second order in general unbounded domains of IR.

A Quantitative Comparison Theorem for Nonlinear Equations

In the present paper we establish a quantitative comparison theorem for positive solutions of the following initial value problems 8 < : (p 1 (r)(u)ju 0 j m?2 u 0) 0 + q 1 (r)f(u) = 0 u(0) = u 0 ; u 0 (0) = 0 and 8 < : (p 2 (r)(v)jv 0 j m?2 v 0) 0 + q 2 (r)f(v) = 0 v(0) = v 0 ; v 0 (0) = 0 with r > 0 and m > 1, and also show some applications of the theorem to the non-existence problem of posit...

Interface Relaxation Methods for Elliptic Differential Equations

A population of eight non-overlapping domain decomposition methods for solving elliptic differential equations are viewed and formulated as iterated interface relaxation procedures. A comprehensive review of the underlying mathematical ideas and the computational characteristics is given. The existing theoretical results are also reviewed and high level descriptions of the various algorithms ar...