کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590686 | 1334976 | 2012 | 29 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Uniqueness of weighted Sobolev spaces with weakly differentiable weights
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Uniqueness of weighted Sobolev spaces with weakly differentiable weights Uniqueness of weighted Sobolev spaces with weakly differentiable weights](/preview/png/4590686.png)
چکیده انگلیسی
We prove that weakly differentiable weights w which, together with their reciprocals, satisfy certain local integrability conditions, admit a unique associated first-order p-Sobolev space, that isH1,p(Rd,wdx)=V1,p(Rd,wdx)=W1,p(Rd,wdx), where dâN and pâ[1,â). If w admits a (weak) logarithmic gradient âw/w which is in Llocq(wdx;Rd), q=p/(pâ1), we propose an alternative definition of the weighted p-Sobolev space based on an integration by parts formula involving âw/w. We prove that weights of the form exp(âβ|â
|qâWâV) are p-admissible, in particular, satisfy a Poincaré inequality, where βâ(0,â), W, V are convex and bounded below such that |âW| satisfies a growth condition (depending on β and q) and V is bounded. We apply the uniqueness result to weights of this type. The associated nonlinear degenerate evolution equation is also discussed.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 263, Issue 10, 15 November 2012, Pages 3195-3223
Journal: Journal of Functional Analysis - Volume 263, Issue 10, 15 November 2012, Pages 3195-3223
نویسندگان
Jonas M. Tölle,