Viscosity solutions, ends and ideal boundaries
نویسندگان
چکیده
منابع مشابه
Viscosity Solutions
Lu = aij(x)Diju for u ∈ C(Ω). Suppose u ∈ C(Ω) is a supersolution in Ω, i.e. Lu ≤ 0. Then if φ ∈ C(Ω) satisfies Lφ > 0, we get L(u− φ) < 0 in Ω, hence by the maximum principle, u− φ does not have interior local minima in Ω. Put differently, if φ ∈ C(Ω) is such that u− φ has a local minimum at x0 ∈ Ω, then necessarily Lφ(x0) ≤ 0. Geometrically, u− φ having a local minimum at x0 means that the gr...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2016
ISSN: 0019-2082
DOI: 10.1215/ijm/1499760017