A global differentiability result for solutions of nonlinear elliptic problems with controlled growths
Czechoslovak Mathematical Journal (2008)
- Volume: 58, Issue: 1, page 113-129
- ISSN: 0011-4642
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topFattorusso, Luisa. "A global differentiability result for solutions of nonlinear elliptic problems with controlled growths." Czechoslovak Mathematical Journal 58.1 (2008): 113-129. <http://eudml.org/doc/31202>.
@article{Fattorusso2008,
abstract = {Let $\Omega $ be a bounded open subset of $\mathbb \{R\}^\{n\}$, $n>2$. In $\Omega $ we deduce the global differentiability result \[ u \in H^\{2\}(\Omega , \mathbb \{R\}^\{N\}) \]
for the solutions $u \in H^\{1\}(\Omega , \mathbb \{R\}^\{n\})$ of the Dirichlet problem \[ u-g \in H^\{1\}\_\{0\}(\Omega , \mathbb \{R\}^\{N\}), -\sum \_\{i\}D\_\{i\}a^\{i\}(x,u,Du)=B\_\{0\}(x,u,Du) \]
with controlled growth and nonlinearity $q=2$. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.},
author = {Fattorusso, Luisa},
journal = {Czechoslovak Mathematical Journal},
keywords = {global differentiability of weak solutions; elliptic problems; controlled growth; nonlinearity with $q=2$; elliptic problems; controlled growth; nonlinearity with },
language = {eng},
number = {1},
pages = {113-129},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A global differentiability result for solutions of nonlinear elliptic problems with controlled growths},
url = {http://eudml.org/doc/31202},
volume = {58},
year = {2008},
}
TY - JOUR
AU - Fattorusso, Luisa
TI - A global differentiability result for solutions of nonlinear elliptic problems with controlled growths
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 1
SP - 113
EP - 129
AB - Let $\Omega $ be a bounded open subset of $\mathbb {R}^{n}$, $n>2$. In $\Omega $ we deduce the global differentiability result \[ u \in H^{2}(\Omega , \mathbb {R}^{N}) \]
for the solutions $u \in H^{1}(\Omega , \mathbb {R}^{n})$ of the Dirichlet problem \[ u-g \in H^{1}_{0}(\Omega , \mathbb {R}^{N}), -\sum _{i}D_{i}a^{i}(x,u,Du)=B_{0}(x,u,Du) \]
with controlled growth and nonlinearity $q=2$. The result was obtained by first extending the interior differentiability result near the boundary and then proving the global differentiability result making use of a covering procedure.
LA - eng
KW - global differentiability of weak solutions; elliptic problems; controlled growth; nonlinearity with $q=2$; elliptic problems; controlled growth; nonlinearity with
UR - http://eudml.org/doc/31202
ER -
References
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- 10.1007/BF01765147, Ann. Mat. Pura Appl., 4. Ser. 131 (1982), 75–106. (1982) MR0681558DOI10.1007/BF01765147
- 10.1016/0001-8708(87)90037-5, Adv. Math. 66 (1987), 291–317. (1987) MR0915857DOI10.1016/0001-8708(87)90037-5
- Differentiability and partial Hölder continuity of the solutions of non linear elliptic systems of order with quadratic growth, Ann. Sc. Norm. Super. Pisa Cl. Sci., IV. Ser. 8 (1981), 285–309. (1981) MR0623938
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