کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415203 1334962 2014 34 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Lavrentiev phenomenon for multiple integral scalar variational problems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the Lavrentiev phenomenon for multiple integral scalar variational problems
چکیده انگلیسی

We prove the non-occurrence of Lavrentiev gaps between Lipschitz and Sobolev functions for functionals of the formI(u)=∫ΩF(u,∇u),u|∂Ω=ϕ when ϕ:Rn→R 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 s↦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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 266, Issue 9, 1 May 2014, Pages 5921-5954
نویسندگان
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