Quasiminimizing properties of solutions to Riccati type equations

Martio, Olli

Martio, Olli

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 4, pp. 823-832.

Résumé

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

Publié le : 2019-02-21

MR Zbl

Classification : 35J60, 35J25

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     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},
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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/

Bibliographie
Cité par

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