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1992 | 27 | 2 | 481-497
Tytuł artykułu

Superposition of functions in Sobolev spaces of fractional order. A survey

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
27
Numer
2
Strony
481-497
Opis fizyczny
Daty
wydano
1992
Twórcy
  • Mathematische Fakultät, Friedrich-Schiller-Universität Jena, D-O-6900 Jena, Germany
Bibliografia
  • [1] D. R. Adams and M. Frazier, BMO and smooth truncation in Sobolev spaces, Studia Math. 89 (1988), 241-260.
  • [2] J. Appell and P. Zabreĭko, Nonlinear Superposition Operators, Cambridge Univ. Press, Cambridge 1990.
  • [3] N. Aronszajn and K. T. Smith, Theory of Bessel potentials. I, Ann. Inst. Fourier (Grenoble) 11 (1961), 385-476.
  • [4] G. Bourdaud, Sur les opérateurs pseudo-différentiels à coefficients peu réguliers, Diss., Univ. de Paris Sud, 1983.
  • [5] A. P. Calderón, Lebesgue spaces of functions and distributions, in: Partial Differential Equations, Proc. Sympos. Pure Math. 4, Amer. Math. Soc., 1961, 33-49.
  • [6] T. Cazenave and F. B. Weissler, The Cauchy Problem for the critical nonlinear Schrödinger equation in $H^s$, Nonlinear Anal. 14 (1990), 807-836.
  • [7] B. E. J. Dahlberg, A note on Sobolev spaces, in: Proc. Sympos. Pure Math. 35, Part I, Amer. Math. Soc., 1979, 183-185.
  • [8] P. Drabek and Th. Runst, On the existence of solutions of a semilinear elliptic boundary value problem with superlinear nonlinearities, Z. Anal. Anwendungen 9 (1990), 105-112.
  • [9] D. E. Edmunds and H. Triebel, Remarks on nonlinear elliptic equations of the type $Δu + u = |u|^p + f$ in bounded domains, J. London Math. Soc. (2) 91 (1985), 331-339.
  • [10] J. Franke and T. Runst, On the admissibility of function spaces of type $B_{p,q}^s$ and $F^s_{p,q}$ and boundary value problems for non-linear partial differential equations, Anal. Math. 13 (1987), 3-27.
  • [11] L. Maligranda, Integration of locally Hölder operators, Studia Math. 78 (1984), 289-296.
  • [12] M. Marcus and V. J. Mizel, Complete characterization of functions which act via superposition on Sobolev spaces, Trans. Amer. Math. Soc. 251 (1979), 187-218.
  • [13] J. Marschall, Pseudo-differential operators with nonregular symbols, thesis, FU Berlin, 1985.
  • [14] Y. Meyer, Remarques sur un théorème de J. M. Bony, Rend. Circ. Mat. Palermo (2) Suppl. 1 (1981), 1-20.
  • [15] S. Mizohata, Lectures on the Cauchy Problem, Tata Institute, Bombay 1965.
  • [16] J. Moser, A rapidly convergent iteration method and non-linear differential equations. I, Ann. Scuola Norm. Sup. Pisa 20 (2) (1966), 265-315; II, ibid. 20 (3) (1966), 499-535.
  • [17] L. Nirenberg, On elliptic partial differential equations, ibid. 13 (1959), 115-162.
  • [18] J. Peetre, Interpolation of Lipschitz operators and metric spaces, Mathematica (Cluj) 12 (35) (1970), 325-334.
  • [19] T. Runst, Paradifferential operators in spaces of Triebel-Lizorkin and Besov type, Z. Anal. Anwendungen 4 (1985), 557-573.
  • [20] T. Runst, Mapping properties of non-linear operators in spaces of Triebel-Lizorkin and Besov type, Anal. Math. 12 (1986), 323-346.
  • [21] T. Runst, Solvability of semilinear elliptic boundary value problems in function spaces, in: Surveys on Analysis, Geometry and Mathematical Physics, Teubner-Texte Math. 117, Teubner, Leipzig 1990, 198-292.
  • [22] T. Runst and W. Sickel, Mapping properties of T:f → |f| in Besov-Triebel-Lizorkin spaces and an application to a nonlinear boundary value problem, preprint.
  • [23] W. Sickel, On pointwise multipliers in Besov-Triebel-Lizorkin spaces, in: Seminar Analysis of the Karl-Weierstrass-Institute 1985/86, Teubner-Texte Math. 96, Teubner, Leipzig 1987, 45-103.
  • [24] W. Sickel, On boundedness of superposition operators in spaces of Triebel-Lizorkin type, Czechoslovak Math. J. 39 (114) (1989), 323-347.
  • [25] W. Sickel, Abbildungseigenschaften von Nemytckii-Operatoren in Besov-Triebel-Lizorkin-Räumen und ausgewählte Anwendungen, manuscript.
  • [26] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press., Princeton 1970.
  • [27] R. S. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. Mech. 16 (1967), 1031-1060.
  • [28] F. Szigeti, On Niemitzki operators in Sobolev spaces, Z. Angew. Math. Mech. 63 (5) (1983), T332.
  • [29] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, NorthHolland, Amsterdam, and Deutscher Verlag Wiss., Berlin 1978.
  • [30] H. Triebel, Theory of Function Spaces, Akad. Verlagsges. Geest & Portig K. G., Leipzig 1983 and Birkhäuser, Basel 1983.
  • [31] H. Triebel, Mapping properties of non-linear operators generated by holomorphic ϕ(u) in function spaces of Besov-Sobolev-Hardy type. Boundary value problems for elliptic differential equations of type Δu = f(x) + Φ(u), Math. Nachr. 117 (1984), 193-213.
  • [32] M. Yamazaki, A quasi-homogeneous version of paradifferential operators, I. Boundedness on spaces of Besov type, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 33 (1986), 131-174.
Typ dokumentu
Bibliografia
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