Ukrainian Mathematical Journal

, Volume 47, Issue 1, pp 107–120 | Cite as

On regularity of generalized solutions of the third boundary-value problem for an elliptic difference-differential equation

  • E. L. Tsvetkov


Unlike the case of elliptic differential equations, generalized solutions of elliptic difference-differential equations may be not smooth in a domainQ but remain smooth only in certain subdomainsQ r Q Conditions are considered which are necessary and sufficient for generalized solutions of the third boundary-value problem to preserve smoothness on the boundary of adjacent subdomainsQ r .


Differential Equation Generalize Solution Elliptic Differential Equation 
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  1. 1.
    A. L. Skubachevskii, “The first boundary-value problem for strongly elliptic differential-difference equations,”J. Different. Equat.,63, No. 3, 332–361 (1986).Google Scholar
  2. 2.
    A. L. Skubachevskii and E. L. Tsvetkov, “The second boundary-value problem for elliptic differential-difference equations,”Differents. Uravn.,25, No. 10, 1766–1776 (1989).Google Scholar
  3. 3.
    G. A. Kamenskii and A. D. Myshkis, “On the statement of boundary-value problems for differential equations with deviating argument and several leading terms,”Differents. Uravn.,10, No. 3, 409–418 (1974).Google Scholar
  4. 4.
    A. L. Skubachevskii, “On eigenvalues and eigenfunctions of some nonlocal boundary-value problems,”Differents. Uravn.,25, No. 1, 127–136 (1989).Google Scholar
  5. 5.
    G. G. Onanov and A. L. Skubachevskii, “Differential equations with deviating argument in stationary problems of mechanics of deformed bodies,”Prikl. Mekhanika,15, No. 5, 39–47 (1979).Google Scholar
  6. 6.
    V. P. Mikhailov,Partial Differential Equations [in Russian], Nauka, Moscow (1983).Google Scholar
  7. 7.
    J.-L. Lions and E. Magenes,Problèmes aux Limites Non Homogénes et Applications, Dunod, Paris (1968).Google Scholar
  8. 8.
    E. L. Tsvetkov, “Solvability and spectrum of the third boundary-value problem for an elliptic differential-difference equation,”Mat. Zametki,51, No. 6, 107–114 (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • E. L. Tsvetkov
    • 1
  1. 1.Moscow Aircraft InstituteUSSR

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