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

Solutions u of the Riccati equation -·A(x,u)=b(x)|u| q with A(x,h)·h|h| p and b a bounded function are studied in an open set ΩR n . It is shown that the solutions u are local quasiminimizers whenever p-1qp for p>n and n-1q<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-1qp are also local quasiminimizers. Examples show that the results are quite sharp.

Published online : 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},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {4},
     year = {2013},
     pages = {823-832},
     zbl = {1321.35025},
     mrnumber = {3184570},
     language = {en},
     url = {http://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, Serie 5, Volume 12 (2013) no. 4, pp. 823-832. http://www.numdam.org/item/ASNSP_2013_5_12_4_823_0/

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