Partial Hölder continuity results for solutions of non linear non variational elliptic systems with limit controlled growth

Fattorusso, Luisa, and Idone, Giovanna. "Partial Hölder continuity results for solutions of non linear non variational elliptic systems with limit controlled growth." Bollettino dell'Unione Matematica Italiana 5-B.3 (2002): 747-754. <http://eudml.org/doc/196172>.

@article{Fattorusso2002,
abstract = {Let $\Omega$ be a bounded open subset of $R^\{n\}$, $n > 4$, of class $C^\{2\}$ . Let $u\in H^\{2\}(\Omega)$ a solution of elliptic non linear non variational system $$a(x, u, Du, H(u) )=b(x, u, Du)$$ where $a(x, u, \mu, \xi)$ and $b(x, u, \mu)$ are vectors in $R^\{N\}$, $N\geq 1$, measurable in $x$, continuous in $(u, \mu, \xi)$ and $(u, \mu)$ respectively. Here, we demonstrate that if $b(x, u, \mu)$ has limit controlled growth, if $a(x, u, \mu, \xi)$ is of class $C^\{1\}$ in $\xi$ and satisfies the Campanato condition $(A)$ and, together with $\frac\{\partial a\}\{\partial \xi\}$, certain continuity assumptions, then the vector $Du$ is partially Hölder continuous for every exponent $\alpha < 1-\frac\{n\}\{p\}$.},
author = {Fattorusso, Luisa, Idone, Giovanna},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {747-754},
publisher = {Unione Matematica Italiana},
title = {Partial Hölder continuity results for solutions of non linear non variational elliptic systems with limit controlled growth},
url = {http://eudml.org/doc/196172},
volume = {5-B},
year = {2002},
}

TY - JOUR
AU - Fattorusso, Luisa
AU - Idone, Giovanna
TI - Partial Hölder continuity results for solutions of non linear non variational elliptic systems with limit controlled growth
JO - Bollettino dell'Unione Matematica Italiana
DA - 2002/10//
PB - Unione Matematica Italiana
VL - 5-B
IS - 3
SP - 747
EP - 754
AB - Let $\Omega$ be a bounded open subset of $R^{n}$, $n > 4$, of class $C^{2}$ . Let $u\in H^{2}(\Omega)$ a solution of elliptic non linear non variational system $$a(x, u, Du, H(u) )=b(x, u, Du)$$ where $a(x, u, \mu, \xi)$ and $b(x, u, \mu)$ are vectors in $R^{N}$, $N\geq 1$, measurable in $x$, continuous in $(u, \mu, \xi)$ and $(u, \mu)$ respectively. Here, we demonstrate that if $b(x, u, \mu)$ has limit controlled growth, if $a(x, u, \mu, \xi)$ is of class $C^{1}$ in $\xi$ and satisfies the Campanato condition $(A)$ and, together with $\frac{\partial a}{\partial \xi}$, certain continuity assumptions, then the vector $Du$ is partially Hölder continuous for every exponent $\alpha < 1-\frac{n}{p}$.
LA - eng
UR - http://eudml.org/doc/196172
ER -