Decay of eigenfunctions of elliptic PDEs, II

TL;DR

This paper investigates how eigenfunctions of higher order elliptic operators decay exponentially in different directions, revealing that decay rates are largely governed by algebraic properties.

Contribution

It provides a detailed analysis of directional decay rates of eigenfunctions, highlighting their algebraic determination, extending previous understanding of elliptic PDE eigenfunction behavior.

Findings

Decay rates depend on direction in space.

Algebraic properties largely determine decay rates.

Results extend previous decay estimates for elliptic operators.

Abstract

We study exponential decay rates of eigenfunctions of self-adjoint higher order elliptic operators on R^n. We are interested in decay rates as a function of direction. We show that the possible decay rates are to a large extent determined algebraically.