کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8898720 1631496 2018 31 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Second order smoothness of weak solutions of degenerate linear equations
ترجمه فارسی عنوان
صافی بودن مرتبه دوم از راه حل های ضعیف معادلات خطی منحرف
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
Let m and n be positive integers and {Yk(x)}k=1m be a collection of m first order Lipschitz vector field derivatives in a bounded open set Ω⊂Rn. Given a real-valued function b in Ω, we find conditions guaranteeing that a weak solution u of ∑k=1mYk′Yku=b in Ω has some second order smoothness. More precisely, if Z is a first order vector field derivative, we study when the iterated weak derivatives ZYku exist in Ω and belong to Lloc2(Ω). The main theorem extends a result of the author for the special case when m=n and Z=Yi for some i. Corollaries include the existence of ZXju, j=1,…,n, for weak solutions u of divergence form equations div(Q∇u)=b if Q(x) is a nonnegative definite, symmetric n×n matrix and {Xj}j=1n are the derivatives corresponding to the rows of Q. The reverse orders YkZu and XjZu are also considered.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 265, Issue 2, 15 July 2018, Pages 671-701
نویسندگان
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