Non-local elliptic problems with non-linear argument transformations near the points of conjugation

Izvestiya Mathematics

Volumn 67, Issue 6, 2003, Pages 1149-1186

  Gurevich, P L ^a  

^a MOSCOW AVIATION INSTITUTE NATIONAL RESEARCH UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21744443785     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM2003v067n06ABEH000460     Document Type: Article

References (46)

1. A. Sommerfeld, "Ein Beitrag zur hydrodinamischcn Erklärung der turbulenten Flussigkeitsbewegungen", Proc. Internat. Congr. Math. (Rome, 1908) vol. 3, Reale Accad. Lincei, Roma, 1909, pp. 116-124.
2. J. D. Tamarkin, Some general problems of the theory of ordinary linear differential equations, and expansion of an arbitrary function in scries of fundamental functions, Petrograd 1917;
3. abridged English transl., Math. Z. 27 (1928), 1-54.
4. M. Picone, "Equazione integrale traducente il più generale problema lineare per le equazioni differenziali lineari ordinarie di qualsivoglia ordine", Atti Accad. Naz. Lincei Rend. Ser. IV 15 (1932), 942-948.
5. T. Carleman, "Sur la théorie des équations intégrales et ses applications", Verhandl. Internat. Math. Kongr. Zürich, vol. 1, 1932, pp. 132-151.
6. A. V. Bitsadze and A. A. Samarskii, "On some simple generalizations of linear elliptic boundary value problems", Dokl. Akad. Nauk SSSR 185 (1969), 739-740;
7. English transl., Soviet Math. Dokl. 10 (1909), 398-400.
8. A. V. Bitsadze, "On a class of conditionally solvable nonlocal boundary value problems for harmonic functions", Dokl. Akad. Nauk SSSR 280 (1985), 521-524;
9. English transl., Soviet Math. Dokl. 31 (1985), 91-94.
10. K. Yu. Kishkis, "The index of a Bitsadze-Samarskii problem for harmonic functions", Differentsial'nye Uravneniya 24 (1988), 105-110;
11. English transl., Differential Equations 24 (1988), 83-87.
12. A. K. Gushchin and V. P. Mikhailov, "On solvability of nonlocal problems for elliptic equations of second order", Mat. Sb. 185:1 (1994), 121-160;
13. English transl., Russian Acad. Sci. Sb. Math. 81 (1995), 101-136.
14. A. L. Skubachevskii, "Elliptic problems with non-local conditions near the boundary", Mat. Sb. 129 (1986), 279-302;
15. English transl., Math. USSR-Sb. 57 (1987), 293-316.
16. A. L. Skubachevskii, "Model nonlocal problems for elliptic equations in dihedral angles", Differentsial'nye Uravneniya 26 (1990), 120-131;
17. English transl., Differential Equations 26 (1990), 106-115.
18. A. L. Skubachevskii, "Truncation-function method in the theory of nonlocal problems", Differentsial'nye Uravneniya 27 (1991), 128-139;
19. English transl., Differential Equations 27 (1991), 103-112.
20. O. A. Kovaleva and A. L. Skubachevskii, "Solvability of nonlocal elliptic problems in weighted spaces", Mat. Zametki 67 (2000), 882-898;
21. English transl., Math. Notes 67 (2000), 743-757.
22. P. L. Gurevich, "Nonlocal problems for elliptic equations in dihedral angles and the Green formula", Mitt. Math. Sem. Giessen 247 (2001), 1-74.
23. P. L. Gurevich, "Asymptotics of solutions for nonlocal elliptic problems in plane angles", Tr. Semin, im. I. G. Petrovskogo 23 (2003);
24. English transl., to appear in J. Math. Sci.
25. A. L. Skubachevskii, "On the stability of index of nonlocal elliptic problems", J. Math. Anal. Appl. 160 (1991), 323-341.
26. A. A. Samarskii, "On some problems in the theory of differential equations", Differentsial'nye Uravneniya 16 (1980), 1925-1935;
27. English transl., Differential Equations 16 (1981), 1221-1228.
28. W. Feller, "The parabolic differential equations and the associated semi-groups of transformations", Ann. of Math. 55 (1952), 468-519.
29. W. Feller, "Diffusion processes in one dimension", Trans. Amer. Math. Soc. 77 (1954), 1-30.
30. K. Taira, "On the existence of Feller semigroups with boundary conditions", Mem. Amer. Math. Soc. 99 (1992), 1-65.
31. A. D. Ventcel', "On boundary conditions for multidimensional diffusion processes", Tear. Veroyatnost. i Primenen. 4 (1959), 172-185;
32. English transl., Theory Probab. Appl. 4 (1960), 164-177.
33. A. L. Skubachevskii, Elliptic functional differential equations and applications, Birkhäuser, Basel-Boston-Berlin 1997.
34. G. G. Onanov and A. L. Skubachevskii, "Differential equations with displaced arguments in stationary problems in the mechanics of a deformed body", Prikl. Mekh. 15:5 (1979), 39-47;
35. English transl., Soviet Appl. Mech. 15 (1979), 391-397.
36. J.-L. Lions and E. Magenes, Problèmes aux limites non-homogènes et applications, vol. 1, Dunod, Paris 1968; Russian transl., Mir, Moscow 1971; English transl., Springer-Verlag, Berlin 1972.
37. E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton 1970; Russian transl., Mir, Moscow 1973.
38. p-estimates of solutions of elliptic boundary value problems in domains with edges", Trudy Moskov. Mat. Obshch. 37 (1978), 49-93;
39. English transl., Trans. Moscow Math. Soc. 1980, no. 1, 49-97.
40. L. N. Slobodetskii, "Generalized Sobolev spaces and their application to boundary value problems for partial differential equations", Uchen. Zap. Leningrad. Cos. Fed. Inst. 197 (1958), 54-112;
41. English transl., Amer. Math. Soc. Transl. Ser. 2 57 (1966), 207-275.
42. V. A. Kondrat'ev, "Boundary value problems for elliptic equations in domains with conical or angular points", Trudy Moskov. Mat. Obshch. 16 (1967), 209-292;
43. English transl., Trans. Moscow Math. Soc. 16 (1968), 227-313.
44. F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Akademiai Kiado, Budapest 1953;
45. Russian transl., Izdat. Inostr. Lit., Moscow 1954.
46. S. G. Krein, Linear equations in Danach spaces, Nauka, Moscow 1971; English transl., Birkhäuser, Boston 1982.