Asymptotic expansion of the nonlocal heat content

被引：0
|
作者：
Grzywny, Tomasz [1 ]
Lenczewska, Julia [1 ]
机构：
[1] Wroclaw Univ Sci & Technol, Fac Pure & Appl Math, PL-50370 Wroclaw, Poland
来源：
STUDIA MATHEMATICA | 2023年 / 270卷 / 03期
关键词：
asymptotic expansion; characteristic exponent; convolution semi-group; fractional Laplacian; heat content; Holder space; Levy measure; nonlocal operator; perimeter; regular variation; FRACTIONAL LAPLACIANS; PERIMETER;
D O I：
10.4064/sm220831-26-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let (pt)t >= 0 be a convolution semigroup of probability measures on Rd defined by (Rd)integral(ei)(xi,x) p(t)(dx) = e(-t psi(xi)), xi is an element of R-d, and let Omega be an open subset of R-d with finite Lebesgue measure. We consider the quantity H-Omega(t) = integral(Omega) integral(Omega-x) p(t) (dy)dx, called the heat content. We study its asymptotic expansion psi under mild assumptions on in particular in the case of the alpha-stable semigroup.
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页码：339 / 359
页数：22
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