Quasiminimizing properties of solutions to Riccati type equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 823-832.

Solutions $u$ of the Riccati equation $-\nabla ·A\left(x,\nabla u\right)={b\left(x\right)|\nabla u|}^{q}$ with $A\left(x,h\right)·h\approx {|h|}^{p}$ and $b$ a bounded function are studied in an open set $\Omega \subset {\mathbf{R}}^{n}$. It is shown that the solutions $u$ are local quasiminimizers whenever $p-1\le q\le p$ for $p>n$ and $n-1\le q for $p=n$. This extends the results in the author’s earlier paper [8] where the case $p was studied. Continuous solutions in the range $p/n+p-1\le q\le p$ are also local quasiminimizers. Examples show that the results are quite sharp.

Publié le : 2019-02-21
Classification : 35J60,  35J25
@article{ASNSP_2013_5_12_4_823_0,
author = {Martio, Olli},
title = {Quasiminimizing properties of solutions to Riccati type equations},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {823--832},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 12},
number = {4},
year = {2013},
zbl = {1321.35025},
mrnumber = {3184570},
language = {en},
url = {www.numdam.org/item/ASNSP_2013_5_12_4_823_0/}
}
Martio, Olli. Quasiminimizing properties of solutions to Riccati type equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 823-832. http://www.numdam.org/item/ASNSP_2013_5_12_4_823_0/

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