Some properties of weighted Sobolev spaces in + d
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 4, p. 675-693
@article{ASNSP_1999_4_28_4_675_0,
     author = {Krylov, Nicolai V.},
     title = {Some properties of weighted Sobolev spaces in $\mathbb {R}^d\_+$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {4},
     year = {1999},
     pages = {675-693},
     zbl = {0962.46016},
     mrnumber = {1760536},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_4_675_0}
}
Krylov, Nicolai V. Some properties of weighted Sobolev spaces in $\mathbb {R}^d_+$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 4, pp. 675-693. http://www.numdam.org/item/ASNSP_1999_4_28_4_675_0/

[1] S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary problems, Comm. Pure Appl. Math., No. 2, 15 (1961), 119-147. | MR 147774 | Zbl 0109.32701

[2] G. Da Prato - J. Zabczyk, "Stochastic equations in infinite dimensions", Cambridge University Press, New York, NY, 1992. | MR 1207136 | Zbl 0761.60052

[3] P. Grisvard, "Elliptic Problems in nonsmooth domains", Monographs and Studies in Mathematics 24, Pittman, Boston-London-Melbourn, 1985. | MR 775683 | Zbl 0695.35060

[4] M.A. Krasnoselskii - E.I. Pustylnik - P.E. Sobolevskii - P.P. Zabrejko, "Integral operators in spaces of summable functions", Nauka, Moscow, 1966 in Russian; English translation: Noordhoff International Publishing, Leyden, 1976. | MR 206751 | Zbl 0312.47041

[5] S.G. Krein - Ju I. Petunin - E.M. Semenov, "Interpolation of linear operators", Nauka, Moscow, 1978 in Russian; English translation in Translations of Math. Monographs, Vol. 54, Amer. Math. Soc., Providence, RI, 1982. | MR 506343 | Zbl 0493.46058

[6] N.V. Krylov, Parabolic equations in the plane and semigroups, Differentsialnye Uravnenija, No. 12, 5 (1969), 2216-2244 in Russian; English translation in Differential Equations 5 (1969), 1661-1667. | MR 265770 | Zbl 0254.35057

[7] N.V. Krylov, Weighted Sobolev spaces and Laplace's equation and the heat equation in a half space, Comm. Partial Differential Equations, 24 (1999), 1611-1653. | MR 1708104 | Zbl 0934.35032

[8] N.V. Krylov, Some properties of traces for stochastic and deterministic parabolic weighted Sobolev spaces, Preprint No. 99-091, SFB 343, University of Bielefeld. | MR 1837532

[9] N.V. Krylov - S.V. Lototsky, A Sobolev space theory of SPDEs with constant coefficients on a half line, SIAM J. Math. Anal., 30 (1999) (1998 in electronic form http://www.siam.org/journals/sima/30-2/32690.html), 298-325. | MR 1664761 | Zbl 0928.60042

[10] N.V. Krylov - S.V. Lototsky, A Sobolev space theory of SPDEs with constant coefficients in a half space, to appear in SIAM J. Math Anal. | MR 1720129 | Zbl 0943.60047

[11] N.V. Krylov - B.L. Rozovskii, On the Cauchy problem for stochastic linear partial differential equations, Izvestija Acad. Nauk SSSR, ser. math., No. 6, 41 (1977), 1329-1347 in Russian; English translation Math. USSR-Izvestija, No. 6, 11, (1977), 1267-1284. | MR 501350 | Zbl 0396.60058

[12] H. Koch, "Non-Euclidean singular integrals and the porous medium equation", Habilitationsschrift, Facultät für Math., Ruprecht-Karls-Universität, Heidelberg, 1998.

[13] J.-L. Lions - E. Magenes, "Problèmes aux limites non homogènes et applications, I", Dunod, Paris, 1968. | Zbl 0165.10801

[14] R.T. Seeley, Complex powers of an elliptic operator, In: "Proc. of Symposia in Pure Math.", Vol. 10, American Math. Soc, Providence, RI, 1967. | MR 237943 | Zbl 0159.15504

[15] V.A. Solonnikov, Solvability of the classical initial-boundary-value problems for the heat-conduction equation in a dihedral angle, Zapiski Nauchnykh Seminarov LOMI, 138 (1984), 146-180 in Russian; English translation in Journal of Soviet Math., No. 5, 32 (1986), 526-546. | MR 755915 | Zbl 0582.35055

[16] E.M. Stein, "Harmonic analysis: real-variable methods, orthogonality and oscillatory integrals", Princeton Univ. Press, Princeton, NJ, 1993. | MR 1232192 | Zbl 0821.42001

[17] H. Triebel, "Theory of function spaces II", Birkhäuser Verlag, Basel-Boston- Berlin, 1992. | MR 1163193 | Zbl 0763.46025

[18] K. Yosida, "Functional analysis", Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. | Zbl 0126.11504