کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6415066 1334910 2016 37 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Estimates of first and second order shape derivatives in nonsmooth multidimensional domains and applications
ترجمه فارسی عنوان
برآورد مشتقات شکل مرتبه اول و دوم در حوزه ها و برنامه های چند بعدی چندگانه
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDEs around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform exterior ball condition. We prove rather sharp continuity results for these shape derivatives with respect to Sobolev norms of the boundary-traces of the displacements. With respect to previous results of this kind, the approach is quite different and is valid in any dimension N≥2. It is based on sharp regularity results for Poisson-type equations in such nonsmooth domains. We also enlarge the class of functionals and PDEs for which these estimates apply. Applications are given to qualitative properties of shape optimization problems under convexity constraints for the variable domains or their complement.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 270, Issue 7, 1 April 2016, Pages 2616-2652
نویسندگان
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