Global Lipschitz continuity for minima of degenerate problems

Content Provider	Semantic Scholar
Author	Bousquet, Pierre Brasco, Lorenzo
Copyright Year	2015
Abstract	We consider the problem of minimizing the Lagrangian $$\int [F(\nabla u)+f\,u]$$∫[F(∇u)+fu] among functions on $$\Omega \subset \mathbb {R}^N$$Ω⊂RN with given boundary datum $$\varphi $$φ. We prove Lipschitz regularity up to the boundary for solutions of this problem, provided $$\Omega $$Ω is convex and $$\varphi $$φ satisfies the bounded slope condition. The convex function F is required to satisfy a qualified form of uniform convexity only outside a ball and no growth assumptions are made.
Starting Page	1403
Ending Page	1450
Page Count	48
File Format	PDF HTM / HTML
DOI	10.1007/s00208-016-1362-9
Volume Number	366
Alternate Webpage(s)	https://hal.archives-ouvertes.fr/hal-01144517/document
Alternate Webpage(s)	https://arxiv.org/pdf/1504.06101v1.pdf
Alternate Webpage(s)	https://www.researchgate.net/profile/Lorenzo_Brasco/publication/271521611_Global_Lipschitz_continuity_for_minima_of_degenerate_problems/links/54cb4afb0cf22f98631e6c06.pdf?origin=publication_list
Alternate Webpage(s)	https://doi.org/10.1007/s00208-016-1362-9
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article