Diferencia entre revisiones de «Espacio de Sóbolev»

* Los espacios de Sóbolev son reflexivos, es decir isomorfos a su [[espacio dual|espacio bidual]], para <math>\scriptstyle 1 < p < \infty</math>

* El espacio de Sóbolev <math>\textstyle W^{0,p}(\Omega) = L^p(\Omega)</math>

* <math>\textstyle W^{m,p}(\Omega) \hookrightarrow \hookrightarrow W^{k,p}(\Omega)</math> si <math>\textstyle m>k</math>

* <math>\textstyle C^m(\bar\Omega) \hookrightarrow W^{m,p}(\Omega)</math>

* <math>\textstyle C^\infty(\bar\Omega) \cap W^{m,p}(\Omega)</math> es [[conjunto denso|denso]] en <math>\textstyle W^{m,p}(\Omega)</math>

* R. A. Adams (1975): ''Sobolev Spaces'', Academic Press, New York, 1975.

* R. Dautray & J.L. Lions, ''Mathematical Analysis and Numerical Methods for Science and Technology, Vol II, Functional and Variational Methods'', Springer-Verlag, Nwe York, 1988.

* S.L. Sobolev, "On a theorem of functional analysis" Transl. Amer. Math. Soc. (2) , 34 (1963) pp. 39–68 Mat. Sb. , 4 (1938) pp. 471–497

* S.L. Sobolev, "Some applications of functional analysis in mathematical physics" , Amer. Math. Soc. (1963)

* E. Zeidler, ''Nonlinear Functional Analysis and its Applications. I: Fixed-point Theorems'', Springer-Verlag, New York, 1985.

* E. Zeidler, ''Nonlinear Functional Analysis and its Applications. IIA: Fixed-point Theorems'', Springer-Verlag, New York, 1990.

* E. Zeidler, ''Nonlinear Functional Analysis and its Applications. III: Fixed-point Theorems'', Springer-Verlag, New York, 1986.

[[de:SobolewSobolev-Raum]]