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  4. Verification algorithm for Lopatynsky condition

Verification algorithm for Lopatynsky condition

MMC.
2024;
Volume 11, Number 4
: pp. 1189–1197
https://doi.org/10.23939/mmc2024.04.1189
Received: April 18, 2024
Revised: April 25, 2024
Accepted: December 03, 2024

Ilkiv V. S., Kalenyuk P. I.  Verification algorithm for Lopatynsky condition.  Mathematical Modeling and Computing. Vol. 11, No. 4, pp. 1189–1197 (2024)

Authors:
  1. V. S. Ilkiv
  2. P. I. Kalenyuk
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University

Authors studied the Lopatynsky condition to single out among properly elliptic differential equations in the Douglis–Nirenberg sense those ones with given boundary conditions that generate an elliptic problem.  This condition can be written in various ways, in particular, in algebraic form also.  A new algebraic formulation of this condition is found and an algorithm for its verification is presented.  Examples of its verification are given as well.

elliptic systems
Douglis–Nirenberg elliptic systems
elliptic boundary value problems
Lopatynsky condition
complementing condition
Bitsadze system
Laplace operator
Navier–Stokes system
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