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On the dimension of the kernel of the Dirichlet problem for fourth-order equations

On the dimension of the kernel of the Dirichlet problem for fourth-order equations We study the dimension of the kernel of the Dirichlet problem in the disk for fourth-order elliptic equations with constant complex coefficients in general position. Special attention is paid to improperly elliptic equations, because the kernel of the Dirichlet problem for properly elliptic equations is finite-dimensional. We single out classes of improperly elliptic equations that have properties similar to those of properly elliptic equations: the kernel of the Dirichlet problem is also finite-dimensional and in some cases even trivial. We consider fourth-order equations in general position, including equations of principal type as well as equations that have multiple characteristics and whose characteristic equation has roots ±i. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the dimension of the kernel of the Dirichlet problem for fourth-order equations

Differential Equations , Volume 51 (4) – May 5, 2015

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References (20)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266115040059
Publisher site
See Article on Publisher Site

Abstract

We study the dimension of the kernel of the Dirichlet problem in the disk for fourth-order elliptic equations with constant complex coefficients in general position. Special attention is paid to improperly elliptic equations, because the kernel of the Dirichlet problem for properly elliptic equations is finite-dimensional. We single out classes of improperly elliptic equations that have properties similar to those of properly elliptic equations: the kernel of the Dirichlet problem is also finite-dimensional and in some cases even trivial. We consider fourth-order equations in general position, including equations of principal type as well as equations that have multiple characteristics and whose characteristic equation has roots ±i.

Journal

Differential EquationsSpringer Journals

Published: May 5, 2015

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