$L^p$-approximation of Jacobians

Malý, Jan. "$L^p$-approximation of Jacobians." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 659-666. <http://eudml.org/doc/247295>.

@article{Malý1991,
abstract = {The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from $\operatorname\{Cart\}^p(\Omega ,\mathbf \{R\}^m)$ is approximated by $\mathcal \{C\} ^1$ functions strongly in $\mathcal \{A\}^q(\Omega ,\mathbf \{R\}^m)$ whenever $q<p$. An example is shown of a function which is in $\operatorname\{cart\}^p(\Omega ,\mathbf \{R\}^2)$ but not in $\operatorname\{cart\}^p(\Omega ,\mathbf \{R\}^2)$.},
author = {Malý, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Sobolev spaces; minors of the Jacobi matrix; weak and strong convergence; cartesian currents; Sobolev space; approximation; smooth functions; nonlinear function spaces},
language = {eng},
number = {4},
pages = {659-666},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$L^p$-approximation of Jacobians},
url = {http://eudml.org/doc/247295},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Malý, Jan
TI - $L^p$-approximation of Jacobians
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 4
SP - 659
EP - 666
AB - The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from $\operatorname{Cart}^p(\Omega ,\mathbf {R}^m)$ is approximated by $\mathcal {C} ^1$ functions strongly in $\mathcal {A}^q(\Omega ,\mathbf {R}^m)$ whenever $q<p$. An example is shown of a function which is in $\operatorname{cart}^p(\Omega ,\mathbf {R}^2)$ but not in $\operatorname{cart}^p(\Omega ,\mathbf {R}^2)$.
LA - eng
KW - Sobolev spaces; minors of the Jacobi matrix; weak and strong convergence; cartesian currents; Sobolev space; approximation; smooth functions; nonlinear function spaces
UR - http://eudml.org/doc/247295
ER -