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A note on the Bitsadze-Samarskii type nonlocal boundary value problem in a Banach space. (English) Zbl 1154.34026
The author studies a boundary value problem for a second-order differential equation in a Banach space. Well-posedness results and coercive type estimates for solutions are obtained in suitable Hölder spaces. As applications, three boundary value problems for elliptic equations are considered.

MSC:
34G10Linear ODE in abstract spaces
35J25Second order elliptic equations, boundary value problems
35J40Higher order elliptic equations, boundary value problems
34B15Nonlinear boundary value problems for ODE
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References:
[1] Agarwal, R.; Bohner, M.; Shakhmurov, V. B.: Maximal regular boundary value problems in Banach-valued weighted spaces, Bound. value probl. 1, 9-42 (2005) · Zbl 1081.35129 · doi:10.1155/BVP.2005.9
[2] Agmon, S.: Lectures on elliptic boundary value problems, (1965) · Zbl 0142.37401
[3] Agmon, S. S.; Douglis, A.; Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. pure appl. Math. 17, 35-92 (1964) · Zbl 0123.28706 · doi:10.1002/cpa.3160170104
[4] Aibeche, A.; Favini, A.: Coerciveness estimate for Ventcel boundary value problem for a differential equation, Semigroup forum 70, No. 2, 269-277 (2005) · Zbl 1081.34013 · doi:10.1007/s00233-004-0170-9
[5] Ashyralyev, A.: Well-posedness of the elliptic equations in a space of smooth functions, Bound. value probl. 2, No. 2, 82-86 (1989)
[6] A. Ashyralyev, Method of positive operators of investigations of the high order of accuracy difference schemes for parabolic and elliptic equations, Doctor Sciences Thesis, Kiev, 1992 (in Russian)
[7] Ashyralyev, A.: Well-posed solvability of the boundary value problem for difference equations of elliptic type, Nonlinear anal. 24, No. 2, 251-256 (1995) · Zbl 0818.65046 · doi:10.1016/0362-546X(94)E0003-Y
[8] Ashyralyev, A.: On well-posedness of the nonlocal boundary value problem for elliptic equations, Numer. funct. Anal. optim. 24, No. 1 -- 2, 1-15 (2003) · Zbl 1055.35018 · doi:10.1081/NFA-120020240
[9] Ashyralyev, A.: Nonlocal boundary value problems for partial differential equations: well-posedness, AIP conf. Proc. 729, 325-331 (2004) · Zbl 1119.35336
[10] Ashyralyev, A.: Fractional spaces generated by the positive differential and difference operators in a Banach space, , 10-19 (2006)
[11] Ashyralyev, A.; Altay, N.: A note on the well-posedness of the nonlocal boundary value problem for elliptic difference equations, Appl. math. Comput. 175, No. 1, 49-60 (2006) · Zbl 1094.39004 · doi:10.1016/j.amc.2005.07.013
[12] Ashyralyev, A.; Amanov, K.: On coercive estimates in hölder norms, Izv. akad. Nauk turkmen. SSR. ser. Fiz.-tekn.-khim. Geol. nauk (1), 3-10 (1996)
[13] Ashyralyev, A.; Sobolevskii, P. E.: Well-posedness of parabolic difference equations, Oper. theory adv. Appl. 69 (1994)
[14] Ashyralyev, A.; Sobolevskii, P. E.: New difference schemes for partial differential equations, Oper. theory adv. Appl. 148 (2004) · Zbl 1060.65055
[15] Ashyralyev, A.; Sobolevskii, P. E.: Well-posedness of the difference schemes of the high order of accuracy for elliptic equations, Discrete dyn. Nat. soc. 2006, 1-12 (2006) · Zbl 1102.65085 · doi:10.1155/DDNS/2006/75153
[16] Ashyralyev, A.; Cuevas, Claudio; Piskarev, S.: On well-posedness of difference schemes for abstract elliptic problems in $Lp([0,1],E)$ spaces, Numer. funct. Anal. optim. 29, No. 1 -- 2, 43-65 (2008) · Zbl 1140.65073 · doi:10.1080/01630560701872698
[17] Berikelashvili, G.: On a nonlocal boundary value problem for a two-dimensional elliptic equation, Comput. methods appl. Math. 3, No. 1, 35-44 (2003) · Zbl 1046.65084 · http://www.cmam.info/issues/?Vol=3&Num=1&ItID=52
[18] Bitsadze, A. V.; Samarskii, A. A.: On some simplest generalizations of linear elliptic problems, Dokl. akad. Nauk SSSR 185 (1969) · Zbl 0187.35501
[19] Clement, Ph.; Guerre-Delabrire, S.: On the regularity of abstract Cauchy problems and boundary value problems, Atti accad. Naz. lincei cl. Sci. fis. Mat. natur. Rend. lincei (9) mat. Appl. 9, No. 4, 245-266 (1998) · Zbl 0928.34042
[20] Gershteyn, L. M.; Sobolevskii, P. E.: Well-posedness of the general boundary value problem for the second order elliptic equations in a Banach space, Differ. equ. 11, No. 7, 1335-1337 (1975)
[21] Gorbachuk, V. L.; Gorbachuk, M. L.: Boundary value problems for differential-operator equations, (1984) · Zbl 0567.47041
[22] Gordeziani, D. G.: On a method of resolution of Bitsadze -- Samarskii boundary value problem, Abstracts of reports of inst. Appl. math. Tbilisi state univ. 2, 38-40 (1970)
[23] Gordeziani, D. G.: On methods of resolution of a class of nonlocal boundary value problems, (1981) · Zbl 0464.35037
[24] Grisvard, P.: Elliptic problems in nonsmooth domains, (1986) · Zbl 0622.34066
[25] Il’in, V. A.; Moiseev, E. I.: Two-dimensional nonlocal boundary value problems for Poisson’s operator in differential and difference variants, Mat. mod. 2, 139-159 (1990) · Zbl 0993.35500
[26] Kapanadze, D. V.: On the Bitsadze -- Samarskii nonlocal boundary value problem, Differ. equ. 23, 543-545 (1987) · Zbl 0657.35046
[27] Krein, S. G.: Linear differential equations in Banach space, (1966) · Zbl 0168.10801
[28] Ladyzhenskaya, O. A.; Ural’tseva, N. N.: Linear and quasilinear equations of elliptic type, (1973) · Zbl 0269.35029
[29] Paneyakh, B. P.: On some nonlocal boundary value problems for linear differential operators, Mat. zametki 35, 425-433 (1984) · Zbl 0553.35020 · doi:10.1007/BF01139921
[30] Pao, C. V.: Reaction diffusion equations with nonlocal boundary and nonlocal initial conditions, J. math. Anal. appl. 195, 702-718 (1995) · Zbl 0851.35063 · doi:10.1006/jmaa.1995.1384
[31] Shakhmurov, V. B.: Coercive boundary value problems for regular degenerate differential-operator equations, J. math. Anal. appl. 292, No. 2, 605-620 (2004) · Zbl 1060.35045 · doi:10.1016/j.jmaa.2003.12.032
[32] Skubachevskii, A. L.: Nonlocal elliptic problems and multidimensional diffusion processes, J. math. Phys. 3, 327-360 (1995) · Zbl 0908.35032
[33] Skubachevskii, A. L.: Elliptic functional differential equations and applications, Oper. theory adv. Appl. 91 (1997) · Zbl 0946.35113
[34] Sobolevskii, P. E.: On elliptic equations in a Banach space, Differ. uravn. 4, No. 7, 1346-1348 (1969)
[35] Sobolevskii, P. E.: The coercive solvability of difference equations, Dokl. acad. Nauk SSSR 201, No. 5, 1063-1066 (1971) · Zbl 0246.39002
[36] Sobolevskii, P. E.: The theory of semigroups and the stability of difference schemes in operator theory in function spaces, , 304-307 (1977)
[37] Sobolevskii, P. E.: Well-posedness of difference elliptic equations, Discrete dyn. Nat. soc. 1, 219-231 (1997) · Zbl 0928.39002 · doi:10.1155/S1026022697000228
[38] Sobolevskii, P. E.; Tiunchik, M. E.: On the well-posedness of the second boundary value problem for difference equations in weighted hölder norms, , 27-37 (1982)
[39] Vishik, M. L.; Myshkis, A. D.; Oleinik, O. A.: Partial differential equations, , 563-599 (1959)