Author:
Gargiulo Giuliano,Zappale Elvira
Abstract
AbstractWe present a sufficient condition ensuring lower semicontinuity for nonlocal supremal functionals of the type "Equation missing"where $$\Omega $$
Ω
is a bounded open subset of $${\mathbb {R}}^N$$
R
N
and $$W:\Omega \,{\times }\, \Omega \,{\times }\, {\mathbb {R}}^{d \times N}{\times }\, {\mathbb {R}}^{d \times N} \rightarrow {\mathbb {R}}.$$
W
:
Ω
×
Ω
×
R
d
×
N
×
R
d
×
N
→
R
.
Funder
Università degli Studi di Roma La Sapienza
Publisher
Springer Science and Business Media LLC
Reference30 articles.
1. Ansini, N., Prinari, F.: On the lower semicontinuity of supremal functional under differential constraints. ESAIM Control Optim. Calc. Var. 21(4), 1053–1075 (2015)
2. Antil, H., Di, Z.W., Khatri, R.: Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography. Inverse Problems 36(6), Art. No. 064001 (2020)
3. Ayanbayev, B., Katzourakis, N.: Vectorial variational principles in $$L^\infty $$ and their characterisation through PDE systems. Appl. Math. Optim. 83(2), 833–848 (2021)
4. Barron, E.N.: Viscosity solutions and analysis in $$L^\infty $$. In: Clarke, F.H., et al. (eds.) Nonlinear Analysis, Differential Equations and Control. NATO Science Series C: Mathematical and Physical Sciences, vol. 528, pp. 1–60. Kluwer, Dordrecht (1999)
5. Barron, E.N., Jensen, R.R., Wang, C.Y.: Lower semicontinuity of $$L^\infty $$ functionals. Ann. Inst. H. Poincaré C Anal. Non Linéaire 18(4), 495–517 (2001)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献