On well-posedness of the nonlocal boundary value problems for elliptic equations

Numerical Functional Analysis and Optimization

Volumn 24, Issue 1-2, 2003, Pages 1-15

  Ashyralyev, Allaberen ^a,b  

^a FATIH UNIVERSITY   (Turkey)

^b Intl Turkmen Turkish University   (Turkmenistan)

Author keywords

Elliptic equation; Exact Schauder's estimates; Nonlocal boundary value problems; Sobolevskii's coercive inequality

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; FUNCTIONS; MATHEMATICAL OPERATORS; OPTIMIZATION; THEOREM PROVING;

ELLIPTIC EQUATIONS;

BOUNDARY VALUE PROBLEMS;

EID: 0037592738     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1081/NFA-120020240     Document Type: Article

References (19)

1. Ashyralyev, A. (1989). Well-posedness of the elliptic equations in a space of smooth functions. Boundary value problems for nonclassic equations of mathematical physics, Sibirsk, Otdel, SSSR- Novosibirsk 2(2):82-86(Russian).
2. Ashyralyev, A. (1990). On the uniform difference schemes of a higher order of the approximation for the elliptic equations with a small parameter. Applicable Analysis 36:211-220.
3. Ashyralyev, A. (1991). Method of Positive Operators of Investigations of High Order of Accuracy Difference Schemes for Parabolic and Elliptic Equations. Doctor Sciences Thesis (Russian). Ashgabat.
4. Ashyralyev, A., Amanov, K. (1995). On Coercive Solvability of Second Boundary Value Problem for Elliptic Equations. TSAU, Preprint: Ashgabat. (Russian).
5. Ashyralyev, A., Amanov, K. (1996). On coercive estimates in Holder Norms, Izv, Akad. Nauk Turkmen. SSR. Ser. Fiz.-Tekn.-Khim. Geol Nauk 1:3-10(Russian).
6. Ashyralyev, A., Karakaya, I. (1995). The Structure of Fractional Spaces Generated by the Positive Operator. Abstracts of the Conference of Young Scientists, p. 15.
7. h of one-dimensional difference operators with nonlocal boundary conditions. Some Problems of Applied Mathematics. Istanbul: Fatih University, 56-70.
8. Ashyralyev, A., Kendirli, B. (2001). Positivity in Holder norms of one- dimensional difference operators with nonlocal boundary conditions. Proceeding of the XXVI Summer School "Application of Mathematics in Engineering and Economics". Sofia: Heron Press, 134-137.
9. Ashyralyev, A., Kendirli, B. (2002). Well-posedness of the nonlocal boundary value problem for elliptic equations. Functional Differential Equations 9:35-55.
10. Ashyralyev, A., Samovik, I. E. (1982). Coercive solvability of the nonlocal boundary value problem for elliptic equations. Trudy Instituta MM AN Turkmenistan 3:67-75(Russian).
11. Ashyralyev, A., Sobolevskii, P. E. (1987). Coercive Stability of a Multidimensional Differential Elliptic Equation of 2m-th Order with Variable Coefficients. Investigations of Differential Equations. Ashgabat: Minvuz Turkmen, SSR. 31-43 (Russian).
12. Ashyralyev, A., Sobolevskii, P. E. (1994). Well-posedness of parabolic difference equations. Basel, Boston, Berlin: Birkhäuser Verlag.
13. Gershteyn, L. M., Sobolevskii, P. E. (1974). Well-posedness of the a Banach space. Differensialnyye Uravneniya 10(11):2059-2061(Russian).
14. Gershteyn, L. M., Sobolevskii, P. E. (1975). Well-posedness of the general boundary value problem for the second order elliptic equations in a Banach space. Differensialnyye Uravneniya 11(7):1335-1337(Russian).
15. Grisvard, P. (1986). Elliptic Problems in Nonsmooth Domains. London: Pitman Advanced Publishing Program.
16. Krein, S. G. (1966). Linear Differential Equations in a Banach Space. Moscow: Nauka (Russian).
17. Sobolevskii, P. E. (1969). On elliptic equations in a Banach space. Differensialnyye Uravneniya 4(7):1346-1348(Russian).
18. Sobolevskii, P. E. (1975). The theory of semigroups and the stability of difference schemes. Operator Theory in Function Spaces. Novosibirsk: Proc. School, 304-337(Russian).
19. Sobolevskii, P. E. (1997). Well-posedness of difference elliptic equations. Discrete Dynamics in Nature and Society 1:219-231.