×

zbMATH — the first resource for mathematics

To the 75th birthday of Vsevolod Alekseevich Solonnikov. (English. Russian original) Zbl 1175.01073
J. Math. Sci., New York 159, No. 4, 385-390 (2009); translation from Zap. Nauchn. Semin. POMI 362, 5-14 (2008).
With list of publications (45 items).
MSC:
01A70 Biographies, obituaries, personalia, bibliographies
Biographic References:
Solonnikov, Vsevolod Alekseevich
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] V. A. Solonnikov, ”On boundary-value problems for general linear parabolic systems,” Dokl. Acad. Nauk SSSR, 157, 56–59 (1964). · Zbl 0141.09501
[2] V. A. Solonnikov, ”A priori estimates for second-order equations of parabolic type,” Trudy Mat. Inst. AN SSSR, 70, 133–212 (1964). · Zbl 0168.08202
[3] V. A. Solonnikov, ”Boundary-value problems for linear parabolic systems of differential equations of general type,” Trudy Mat. Inst. AN SSSR, 83, 3–162 (1965). · Zbl 0164.12502
[4] O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type [in Russian], Nauka, Moscow (1964).
[5] W. M. Zajaczkowski and V. A. Solonnikov, ”The Neyman problem for second-order elliptic equations in domains with edges on the boundary,” Zap. Nauchn. Semin. LOMI, 127, 7–18 (1983). · Zbl 0518.35030
[6] V. A. Solonnikov, ”Solvability of classical initial boundary-value problems for the heat equation in a dihedral angle,” Zap. Nauchn. Semin. LOMI, 138, 146–180 (1984). · Zbl 0557.35064
[7] V. A. Solonnikov and E. V. Frolova, ”On the problem with a third boundary-value condition for the Laplace equation in a plane angle and its applications to parabolic problems,” Algebra Analiz, 2, 213–241 (1990). · Zbl 0711.35036
[8] G. I. Bizhanova and V. A. Solonnikov, ”Solvability of the initial boundary-value problem for a second-order parabolic equation with time derivative in the boundary condition in a weighted Hölder function space,” Algebra Analiz, 5, 109–142 (1993). · Zbl 0805.35043
[9] G. I. Bizhanova and V. A. Solonnikov, ”Free boundary problems for second-order parabolic equations,” Algebra Analiz, 12, 98–139 (2000). · Zbl 0997.35102
[10] V. A. Solonnikov and E. V. Frolova, ”On the validity of the quasistationary approximation for the Stefan problem,” Zap. Nauchn. Semin. POMI, 248, 209–253 (2007).
[11] K. K. Golovkin and V. A. Solonnikov, ”Estimates of integral operators in translation-invariant norms,” Trudy Mat. Inst. AN SSSR, 70, 47–58 (1964). · Zbl 0163.33204
[12] K. K. Golovkin and V. A. Solonnikov, ”Estimates of integral operators in translation-invariant norms,” Trudy Mat. Inst. AN SSSR, 92, 5–30 (1966). · Zbl 0167.14901
[13] K. K. Golovkin and V. A. Solonnikov, ”Estimates of convolution operators,” Zap. Nauchn. Semin. LOMI, 7, 6–86 (1968). · Zbl 0205.14602
[14] I. V. Denisova, O. A. Ladyzhenskaya, G. A. Seregin, N. N. Uraltseva, and E. V. Frolova, ”To the jubilee of Vsevolod Alekseevich Solonnikiov,” Zap. Nauchn. Semin. POMI, 306, 7–15 (2003).
[15] V. A. Solonnikov, ”Estimates of solutions to the nonstationary linearized Navier–Stokes system,” Trudy Mat. Inst. AN SSSR, 70, 213–317 (1964). · Zbl 0163.33803
[16] V. A. Solonnikov, ”Differential properties of solutions of the first boundary-value problem for a nonstationary system of Navier–Stokes equations,” Trudy Mat. Inst. AN SSSR, 73, 221–291 (1964). · Zbl 0163.33901
[17] V. A. Solonnikov, ”Estimates of solutions to a nonstationary Navier–Stokes system,” Zap. Nauchn. Semin. LOMI, 38, 153–231 (1973). · Zbl 0346.35083
[18] V. A. Solonnikov, ”Estimates of solutions to the Stokes system in S. L. Sobolev spaces with a mixed norm,” Zap. Nauchn. Semin. POMI, 288, 204–231 (2002). · Zbl 1068.35093
[19] O. A. Ladyzhenskaya and V. A. Solonnikov, ”Solvability of boundary-value and initial boundary-value problems to the Navier–Stokes equations in domains with noncompact boundaries,” Vestn. Leningr. Univ., 13, 39–47 (1977). · Zbl 0377.35060
[20] O. A. Ladyzhenskaya and V. A. Solonnikov, ”Some problems of vector analysis and generalized settings of boundary-value problems for Navier–Stokes equations,” Zap. Nauchn. Semin. LOMI, 59, 81–116 (1976). · Zbl 0346.35084
[21] V. A. Solonnikov and K. I. Pileckas, ”Some spaces of solenoidal vectors and solvability of boundary-value problems for the Navier–Stokes system in domains with noncompact boundaries,” Zap. Nauchn. Semin. LOMI. 79, 136–151 (1977).
[22] O. A. Ladyzhenskaya and V. A. Solonnikov, ”Search for solutions of boundary-values problems for stationary Stokes and Navier–Stokes equations with an unbounded Dirichlet integral,” Zap. Nauchn. Semin. LOMI, 96, 117–160 (1980). · Zbl 0463.35069
[23] V. A. Solonnikov, ”Problems in hydrodynamics of a viscous incompressible fluid in domains with noncompact boundaries,” Algebra Analiz, 4, 28–53 (1992). · Zbl 0840.35078
[24] V. A. Solonnikov and V. E. Shchadilov, ”One boundary-value problem for a stationary Navier–Stokes system,” Trudy Mat. Inst. AN SSSR, 125, 196–210 (1973).
[25] V. A. Solonnikov, ”Solvability of the problem of planar motion for a heavy, viscous, incompressible, capillary fluid that fills part of a vessel,” Izv. Acad. Nauk SSSR, Ser. Mat., 43, 203–236 (1979).
[26] V. A. Solonnikov, ”Solvability of a three-dimensional free boundary problem for the stationary Navier–Stokes system,” Zap. Nauchn. Semin. LOMI, 84, 252–285 (1979). · Zbl 0414.35062
[27] V. A. Solonnikov, ”Solvability of the problem on evolution of a bounded volume of a viscous incompressible capillary fluid,” Zap. Nauchn. Semin. LOMI, 140, 179–186 (1984). · Zbl 0551.76022
[28] V. A. Solonnikov, ”An initial boundary-value problem for the Stokes system that arises in a free boundary problem,” Trudy Mat. Inst. AN SSSR, 188, 150–188 (1990).
[29] V. A. Solonnikov, ”Solvability of the problem on finite-time evolution for a viscous incompressible fluid bounded by a free surface,” Algebra Analiz, 3, 222–257 (1991).
[30] I. Sh. Mogilevskii and V. A. Solonnikov, ”Solvability of a noncoercive initial boundary-value problem for the Stokes system in Hölder function classes,” Z. Anal. Anwendangen, 8, 329–347 (1989). · Zbl 0705.35106
[31] I. Sh. Mogilevskiĭ and V. A. Solonnikov, ”On the solvability of an evolution free boundary problem for the Navier–Stokes equations in Hölder spaces of functions,” in: Mathematical Problems Related to the Navier-Stokes Equations (G. P. Galdi, eds.), vol. 11, World Sci. Publ. (1992), pp. 105–181. · Zbl 0793.35072
[32] V. A. Solonnikov, ”Estimates of solutions of the second initial boundary-value problem for the Stokes system in spaces of functions with Hölder-continuous derivatives in space variables,” Zap. Nauchn. Semin. POMI, 259, 254–279 (1999). · Zbl 1153.76349
[33] V. A. Solonnikov, ”On the justification of the quasistationary approximation in the problem of motion of a viscous capillary drop,” Interfaces and Free Bundaries, 1, 125–173 (1999). · Zbl 0974.35097 · doi:10.4171/IFB/7
[34] I. V. Denisova and V. A. Solonnikov, ”The classical solvability of a model problem in a half-space connected with motion of an isolated mass of compressible fluid,” Zap. Nauchn. Semin. POMI, 271, 92–113 (2000). · Zbl 1118.76312
[35] l. V. Denisova and V. A. Solonnikov, ”The classical solvability of the problem on motion of an isolated mass of compressible fluid,” Algebra Analiz, 14, 71–98 (2002). · Zbl 1037.35103
[36] V. A. Solonnikov, ”Unsteady motion of a finite isolated mass of self-gravitating fluid,” Algebra Analiz, 1, 207–248 (1989). · Zbl 0713.76044
[37] V. A. Solonnikov, ”Evolution free boundary problem for equations of motion of viscous compressible barotropic self-gravitating fluid,” SAACM, 3, 257–275 (1993).
[38] V. A. Solonnikov, ”Estimate of the generalized energy in the free boundary problem for viscous incompressible fluid,” Zap. Nauchn. Semin. POMI, 282, 216–243 (2001). · Zbl 1075.35041
[39] V. A. Solonnikov, ”Stability of axially symmetric equilibrium figures of rotating viscous incompressible fluid,” Algebra Analiz, 16, No. 2 (2004). · Zbl 1075.35042
[40] V. A. Solonnikov, ”Lectures on evolution free boundary problems: classical solutions”, Lect. Notes Math., Springer, 1812, 123–175 (2003). · Zbl 1038.35063
[41] V. A. Solonnikov, ”On instability of axially symmetric equilibrium figures of rotating viscous incompressible liquid,” Zap. Nauchn. Semin. POMI, 318, 277–297 (2004). · Zbl 1075.35042
[42] V. A. Solonnikov, ”On instability of equilibrium figures of rotating viscous incompressible self-gravitating liquid not subjected to capillary forces,” J. Math. Sci., 139, 6338–6350 (2006). · Zbl 1119.35069 · doi:10.1007/s10958-006-0351-z
[43] V. A. Solonnikov, ”On the stability of non-symmetric equilibrium figures of rotating self-gravitating liquid not subjected to capillary forces,” Volume dedicated to A. V. Kazhikhov, book series ”Advances in Mathematical Fluid Mechanics”, Birkhaeuser (to appear in 2009).
[44] I. V. Denisova and V. A. Solonnikov, ”Classical solvability of the problem on motion of two viscous incompressible liquid,” Algebra Analiz, 7, 101–142 (1995). · Zbl 0859.35093
[45] V. A. Solonnikov, ”On the problem of non-stationary motion of two viscous incompressible liquids,” J. Math. Sci., 142, 1844–1866 (2007). · Zbl 1202.35177 · doi:10.1007/s10958-007-0093-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.