کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4669362 | 1346133 | 2006 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the best Sobolev trace constant and extremals in domains with holes
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: On the best Sobolev trace constant and extremals in domains with holes On the best Sobolev trace constant and extremals in domains with holes](/preview/png/4669362.png)
چکیده انگلیسی
We study the dependence on the subset A⊂Ω of the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. First we find that there exists an optimal subset that makes the trace constant smaller among all the subsets with prescribed and positive Lebesgue measure. In the case that Ω is a ball we prove that there exists an optimal hole that is spherically symmetric. In the case p=2 we prove that every optimal hole is spherically symmetric. Then, we study the behavior of the best constant when the hole is allowed to have zero Lebesgue measure. We show that this constant depends continuously on the subset and we discuss when it is equal to the Sobolev trace constant without the vanishing restriction.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 130, Issue 7, October–November 2006, Pages 565-579
Journal: Bulletin des Sciences Mathématiques - Volume 130, Issue 7, October–November 2006, Pages 565-579