کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900307 | 1631560 | 2018 | 32 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Maximal Sobolev regularity for solutions of elliptic equations in Banach spaces endowed with a weighted Gaussian measure: The convex subset case
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Maximal Sobolev regularity for solutions of elliptic equations in Banach spaces endowed with a weighted Gaussian measure: The convex subset case Maximal Sobolev regularity for solutions of elliptic equations in Banach spaces endowed with a weighted Gaussian measure: The convex subset case](/preview/png/8900307.png)
چکیده انگلیسی
Let X be a separable Banach space endowed with a non-degenerate centered Gaussian measure μ. The associated Cameron-Martin space is denoted by H. Consider two sufficiently regular convex functions U:XâR and G:XâR. We let ν=eâUμ and Ω=Gâ1(ââ,0]. In this paper we are interested in the W2,2 regularity of the weak solutions of elliptic equations of the type(0.1)λuâLν,Ωu=f, where λ>0, fâL2(Ω,ν) and Lν,Ω is the self-adjoint operator associated with the quadratic form(Ï,Ï)â¦â«Î©ãâHÏ,âHÏãHdνÏ,ÏâW1,2(Ω,ν). In addition we will show that if u is a weak solution of problem (0.1) then it satisfies a Neumann type condition at the boundary, namely for Ï-a.e. xâGâ1(0)ãTr(âHu)(x),Tr(âHG)(x)ãH=0, where Ï is the Feyel-de La Pradelle Hausdorff-Gauss surface measure and Tr is the trace operator.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 458, Issue 1, 1 February 2018, Pages 300-331
Journal: Journal of Mathematical Analysis and Applications - Volume 458, Issue 1, 1 February 2018, Pages 300-331
نویسندگان
G. Cappa, S. Ferrari,