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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Uniqueness of weighted Sobolev spaces with weakly differentiable weights
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 d∈N and p∈[1,∞). If w admits a (weak) logarithmic gradient ∇w/w which is in Llocq(wdx;Rd), q=p/(p−1), we propose an alternative definition of the weighted p-Sobolev space based on an integration by parts formula involving ∇w/w. We prove that weights of the form exp(−β|⋅|q−W−V) are p-admissible, in particular, satisfy a Poincaré inequality, where β∈(0,∞), W, V are convex and bounded below such that |∇W| 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
نویسندگان
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