We investigate positivity sets of nonnegative supersolutions of the fully nonlinear elliptic equations F(x, u,Du,D2u) = 0 in Ω, where Ω is an open subset of RN, and the validity of the strong maximum principle for F(x, u,Du,D2u) = f in Ω, with f ∈ C(Ω) being nonpositive. We obtain geometric characterizations of positivity sets {x ∈ Ω : u(x) > 0} of nonnegative supersolutions u and establish the strong maximum principle under some geometric assumption on the set {x ∈ Ω : f(x) = 0}.
Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle / Birindelli, Isabella; Galise, Giulio; Ishii, Hitoshi. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 374:(2021), pp. 539-564. [10.1090/tran/8226]
Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle
Birindelli, Isabella;Galise, Giulio;
2021
Abstract
We investigate positivity sets of nonnegative supersolutions of the fully nonlinear elliptic equations F(x, u,Du,D2u) = 0 in Ω, where Ω is an open subset of RN, and the validity of the strong maximum principle for F(x, u,Du,D2u) = f in Ω, with f ∈ C(Ω) being nonpositive. We obtain geometric characterizations of positivity sets {x ∈ Ω : u(x) > 0} of nonnegative supersolutions u and establish the strong maximum principle under some geometric assumption on the set {x ∈ Ω : f(x) = 0}.File | Dimensione | Formato | |
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