Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415203 | Journal of Functional Analysis | 2014 | 34 Pages |
Abstract
We prove the non-occurrence of Lavrentiev gaps between Lipschitz and Sobolev functions for functionals of the formI(u)=â«Î©F(u,âu),u|âΩ=Ï when Ï:RnâR is Lipschitz and Ω belongs to a wide class of open bounded sets in Rn containing Lipschitz domains. The Lagrangian F is assumed to be either convex in both variables or a sum of functions F(s,ξ)=a(s)g(ξ)+b(s) with g convex and sâ¦a(s)g(0)+b(s) satisfying a non-oscillatory condition at infinity. We thus derive the non-occurrence of the Lavrentiev phenomenon for unnecessarily convex functionals of the gradient. No growth conditions are assumed.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pierre Bousquet, Carlo Mariconda, Giulia Treu,