کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4590783 1334983 2013 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Meyers inequality and strong stability for stable-like operators
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Meyers inequality and strong stability for stable-like operators
چکیده انگلیسی

Let α∈(0,2)α∈(0,2), letE(u,u)=∫Rd∫Rd(u(y)−u(x))2A(x,y)|x−y|d+αdydx be the Dirichlet form for a stable-like operator, letΓu(x)=(∫Rd(u(y)−u(x))2A(x,y)|x−y|d+αdy)1/2, let L   be the associated infinitesimal generator, and suppose A(x,y)A(x,y) is jointly measurable, symmetric, bounded, and bounded below by a positive constant. We prove that if u   is the weak solution to Lu=hLu=h, then Γu∈LpΓu∈Lp for some p>2p>2. This is the analogue of an inequality of Meyers for solutions to divergence form elliptic equations. As an application, we prove strong stability results for stable-like operators. If A is perturbed slightly, we give explicit bounds on how much the semigroup and fundamental solution are perturbed.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 265, Issue 1, 1 July 2013, Pages 28–48
نویسندگان
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