منابع مشابه
Hölder Continuity for Local Minimizers of a Nonconvex Variational Problem
|ξ| ≤ f(x, u, ξ) ≤ L(1 + |ξ|). A function u ∈ W 1,p loc (Ω) is a local minimizer of F in Ω if F (u; spt (v − u)) ≤ F (v; spt (v − u)) , for every v ∈ W 1,p loc (Ω) such that spt (v − u) ⊂⊂ Ω. Well known results due to Giaquinta and Giusti [13, 15] ensure that local minimizers of F are locally α-Hölder continuous for some α < 1. According to Meyers’ example in [19], when f is not continuous in Ω...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1999
ISSN: 0022-247X
DOI: 10.1006/jmaa.1999.6410