Access the full text.
Sign up today, get DeepDyve free for 14 days.
AP Soldatov (2003)
On the First and Second Boundary Value Problems for Elliptic Systems on the PlaneDiffer. Uravn., 39
(1983)
Translated under the title Analiz lineinykh differentsial'nykh operatorov s chastnymi proizvodnymi
VP Palamodov (1967)
Lineinye differentsial’nye operatory s postoyannymi koeffitsientami
(1968)
New Statements and Investigations of the First, Second, and Third Boundary Value Problems for Strongly Coupled Elliptic Systems of Two Second Order Differential Equations with Constant Coefficients
(2007)
On the Dirichlet Problem for an Irregular Elliptic Equation of the Fourth Order, in Neklassicheskie uravneniya matematicheskoi fiziki (Nonclassical
(2005)
Some Problems of the Nontrivial Solvability of the Homogeneous Dirichlet Problem for Linear Equations of Arbitrary Even Order in the Disk
AO Babayan (2007)
Neklassicheskie uravneniya matematicheskoi fiziki
(2002)
Metody issledovaniya granichnykh zadach dlya obshchikh differentsial’nykh uravnenii (Methods for Studying Boundary Value Problems for General Differential Equations)
(2000)
On the Uniqueness of Solutions of the Dirichlet Problem for Fourth-Order Differential Equations in a Disk in Degenerate Cases
A. Soldatov (2003)
On the First and Second Boundary Value Problems for Elliptic Systems on the PlaneDifferential Equations, 39
(1983)
The Analysis of Linear Differential Operators
(1951)
On Strongly Elliptic Systems of Differential Equations
problem consists of countably many linearly independent polynomial solutions of the form u n (z) = (1 − zz) 2 P n (z), n = 0, 1, 2, . . . , for k = 3 and u n (z) = (1 − zz) 3 P n (z)
VP Burskii, EA Buryachenko (2012)
Violation of the Uniqueness of the Solution of the Dirichlet Problem for Typeless Differential Equations of Arbitrary Even Order in the DiskUkrain. Mat. Visn., 9
AV Bitsadze (1948)
On the Uniqueness of the Solution of the Dirichlet Problem for Elliptic Partial Differential EquationsUspekhi Mat. Nauk, 3
VP Burskii (1990)
Violation of the Uniqueness of the Solution to the Dirichlet Problem for Elliptic Systems in the DiskMat. Zametki, 48
(2003)
The Dirichlet Problem for a Properly Elliptic Equation in the Unit Disk
VP Burskii (2002)
Metody issledovaniya granichnykh zadach dlya obshchikh differentsial’nykh uravnenii
(1953)
On a Method for Reducing Boundary Problems for a System of Differential Equations of Elliptic Type to Regular Integral Equation
A. Talbot (1972)
LINEAR DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTSBulletin of The London Mathematical Society, 4
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.
Differential Equations – Springer Journals
Published: May 5, 2015
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.