On the fractional differentiability of the spatial derivatives of weak solutions to nonlinear parabolic systems of higher order

Amato, Roberto. "On the fractional differentiability of the spatial derivatives of weak solutions to nonlinear parabolic systems of higher order." Czechoslovak Mathematical Journal 66.2 (2016): 293-305. <http://eudml.org/doc/280096>.

@article{Amato2016,
abstract = {We are concerned with the problem of differentiability of the derivatives of order $m+1$ of solutions to the “nonlinear basic systems” of the type \[ (-1)^m \sum \_\{|\alpha | = m\}D^\{\alpha \} A^\{\alpha \}\big (D^\{(m)\}u\big )+ \frac\{\partial u\}\{\partial t\} = 0 \quad \text\{in\} \ Q. \] We are able to show that \[ D^\{\alpha \}u \in L^2\bigl (-a, 0, H^\{\vartheta \}\big (B(\sigma ),\mathbb \{R\}^N\big )\big ), \quad |\alpha |=m+1, \] for $\vartheta \in (0, \{1\}/\{2\})$ and this result suggests that more regularity is not expectable.},
author = {Amato, Roberto},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear parabolic system; fractional differentiability; spatial derivative; weak solution},
language = {eng},
number = {2},
pages = {293-305},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the fractional differentiability of the spatial derivatives of weak solutions to nonlinear parabolic systems of higher order},
url = {http://eudml.org/doc/280096},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Amato, Roberto
TI - On the fractional differentiability of the spatial derivatives of weak solutions to nonlinear parabolic systems of higher order
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 293
EP - 305
AB - We are concerned with the problem of differentiability of the derivatives of order $m+1$ of solutions to the “nonlinear basic systems” of the type \[ (-1)^m \sum _{|\alpha | = m}D^{\alpha } A^{\alpha }\big (D^{(m)}u\big )+ \frac{\partial u}{\partial t} = 0 \quad \text{in} \ Q. \] We are able to show that \[ D^{\alpha }u \in L^2\bigl (-a, 0, H^{\vartheta }\big (B(\sigma ),\mathbb {R}^N\big )\big ), \quad |\alpha |=m+1, \] for $\vartheta \in (0, {1}/{2})$ and this result suggests that more regularity is not expectable.
LA - eng
KW - nonlinear parabolic system; fractional differentiability; spatial derivative; weak solution
UR - http://eudml.org/doc/280096
ER -