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 Mat. Sb. (N.S.), 1973, Volume 91(133), Number 1(5), Pages 62–77 (Mi msb3104)

Conjugate problems of elliptic differential and pseudodifferential boundary value problems in a bounded domain

A. S. Dikanskii

Abstract: A new class of boundary value problems for elliptic differential and pseudodifferential operators in spaces of generalized functions is studied.
An explicit form is obtained for boundary value problems conjugate to elliptic differential and pseudodifferential boundary value problems in generalized and smooth functions without restrictions on the boundary operators, which permits explicit description of conditions for solvability of the original elliptic problem.
Bibliography: 18 titles.

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English version:
Mathematics of the USSR-Sbornik, 1973, 20:1, 67–83

Bibliographic databases:

UDC: 517.43
MSC: Primary 35J40, 35S15; Secondary 47F05

Citation: A. S. Dikanskii, “Conjugate problems of elliptic differential and pseudodifferential boundary value problems in a bounded domain”, Mat. Sb. (N.S.), 91(133):1(5) (1973), 62–77; Math. USSR-Sb., 20:1 (1973), 67–83

Citation in format AMSBIB
\Bibitem{Dik73} \by A.~S.~Dikanskii \paper Conjugate problems of elliptic differential and pseudodifferential boundary value problems in a~bounded domain \jour Mat. Sb. (N.S.) \yr 1973 \vol 91(133) \issue 1(5) \pages 62--77 \mathnet{http://mi.mathnet.ru/msb3104} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=342852} \zmath{https://zbmath.org/?q=an:0278.35080} \transl \jour Math. USSR-Sb. \yr 1973 \vol 20 \issue 1 \pages 67--83 \crossref{https://doi.org/10.1070/SM1973v020n01ABEH001842} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. L. R. Volevich, S. G. Gindikin, “The method of energy estimates in mixed problems”, Russian Math. Surveys, 35:5 (1980), 57–137
2. Frank-Olme Speck, “Eine Methode zur Lösung mehrdimensionaler Kopplungsprobleme”, Math Nachr, 107:1 (1982), 59
3. R.N Pederson, “Explicit formulas for complementary boundary operators of linear elliptic problems. I. The half-space case”, Journal of Differential Equations, 46:3 (1982), 346
4. Ching-Lung Chang, Max D. Gunzburger, “A finite element method for first order elliptic systems in three dimensions”, Applied Mathematics and Computation, 23:2 (1987), 171
5. C.L. Chang, “A least-squares finite element method for the Helmholtz equation”, Computer Methods in Applied Mechanics and Engineering, 83:1 (1990), 1
6. Ching Lung Chang, “A mixed finite element method for the stokes problem: an acceleration-pressure formulation”, Applied Mathematics and Computation, 36:2 (1990), 135
7. Ching Lung Chang, “Finite Element Approximation for Grad-Div Type Systems in the Plane”, SIAM J Numer Anal, 29:2 (1992), 452
8. Suh-Yuh Yang, Jinn-Liang Liu, “Least-squares finite element methods for the elasticity problem”, Journal of Computational and Applied Mathematics, 87:1 (1997), 39
9. Suh-Yuh Yang, Ching L. Chang, “A two-stage least-squares finite element method for the stress-pressure-displacement elasticity equations”, Numer Methods Partial Differential Eq, 14:3 (1998), 297
10. Suh-Yuh Yang, “Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity-stress-pressure formulation”, Math Meth Appl Sci, 21:18 (1998), 1637
11. Suh-Yuh Yang, Jinn-Liang Liu, “Analysis of least squares finite element methods for a parameter-dependent first-order system*”, Numerical Functional Analysis and Optimization, 19:1-2 (1998), 191
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