It is obtained that there exist strong solutions of Pucci extremal equations with sublinear growth in Du and measurable ingredients. It is proved that a strong maximum principle holds in a local sense in Lemma 4.1 although even the (weak) maximum principle fails. By using this existence result, it is shown that the ABP type maximum principle and the weak Harnack inequality for viscosity solutions hold true. As an application, the Hölder continuity for viscosity solutions of possibly singular, quasilinear equations is established.
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版ステータス||Published - 2017 9 1|
ASJC Scopus subject areas
- Applied Mathematics