Espacio de Sobolev W^(m,p) (Ω) con 1≤p≤+∞
Resumen
En este artículo hacemos una breve revisión de los espacios de Sobolev, para lo cual presentamos su estructura vectorial ligada a los espacios Lp. Además, Se muestran que dichos espacios son normados, de Banach, separables y algunos son reflexivos (i,e; es isomorfo a su bidual) y finalmente se demostrarán los teoremas de inmersión y de aproximación por funciones suaves en dichos espacios.
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Referencias
R.A. Adams, Sobolev Spaces , Academic Press, New York, 1975.
Grisvard, P. (1985), Elliptic Problems in Nonsmooth Domains.
Pitman, Boston.
Stein, E.M. (1970), Singular Integrals and Diferentiability
Properties of Funcrions. Princeton University Press, Princeton.
V.I Burenkov; Mollifying operators with variable step and their applications to approximation by differentiable funtions, In”Nonlinear analysis, funtion spaces and applications”, Teubner-Textezur Mathematik, Leipzig,49 (1982),5-37.
A. Kufner, Weighted Sobolev spaces, John Wiley and Sons 1983.
A.A. Dezin. On embedding theorems and extension problem, Dokl. Akad. Nauk SSSR 88(1953-54),741- 743(Russian).
L.C. Evans, Partial Differential Equations , AMS, Providence, RI, 1998.
A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969.
A. Friedman, Foundations of Modern Analysis, Dover Publications, Inc., New York,1982.
D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order , Springer-Verlag,Berlin, 1983.
D. Kinderlehrer, G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
J.T. Marti, Introductionto Sobolev Spaces and Finite Element Solution of Elliptic Boundary Value Problems, Academic Press, London, 1986.
V.G. Maz’ja, Sobolev Spaces , Springer-Verlag, Berlin, 1985.
C. B. Morrey, Jr., Multiple Integrals in the Calculus of Variations , Springer-Verlag, New York, 1966.
J. Necas, Introduction to the Theory of Nonlinear Elliptic Equations , Teubner, Leipzig, 1983.
J. Necas, Les Méthodes Directes en Théorie des Équations Elliptiques , Academia, Prague, 1967.
L. Nirenberg, Topics in Nonlinear Functional Analysis, Courant Institute, New York, 1974.
S.L. Sobolev, On a theorem of functional analysis, Mat. Sb. 4 (46) 1938, 39-68 (translated into English in 1963).
H. Tanabe, Functional Analytic Methods for Partial Differential
Equations , Dekker, New York, 1997.
H. Triebel, Interpolation Theory, Function Spaces, Differential
Operators , VebDeutscher, Berlin, 1978.
