TY - JOUR

T1 - On operator estimates in homogenization of non-local operators of convolution type

AU - Пятницкий, Андрей Львович

AU - Слоущ, Владимир Анатольевич

AU - Суслина, Татьяна Александровна

AU - Жижина, Елена Анатольевна

PY - 2023/4/15

Y1 - 2023/4/15

N2 - The paper studies a bounded symmetric operator Aε in L2(Rd) with (Aεu)(x)=ε−d−2∫Rda((x−y)/ε)μ(x/ε,y/ε)(u(x)−u(y))dy; here ε is a small positive parameter. It is assumed that a(x) is a non-negative L1(Rd) function such that a(−x)=a(x) and the moments Mk=∫Rd|x|ka(x)dx, k=1,2,3, are finite. It is also assumed that μ(x,y) is Zd-periodic both in x and y function such that μ(x,y)=μ(y,x) and 0

AB - The paper studies a bounded symmetric operator Aε in L2(Rd) with (Aεu)(x)=ε−d−2∫Rda((x−y)/ε)μ(x/ε,y/ε)(u(x)−u(y))dy; here ε is a small positive parameter. It is assumed that a(x) is a non-negative L1(Rd) function such that a(−x)=a(x) and the moments Mk=∫Rd|x|ka(x)dx, k=1,2,3, are finite. It is also assumed that μ(x,y) is Zd-periodic both in x and y function such that μ(x,y)=μ(y,x) and 0

KW - Convolution type operator

KW - Effective operator

KW - Operator estimates

KW - Periodic homogenization

UR - https://www.mendeley.com/catalogue/605e0964-5a66-359b-8960-19f270253ddb/

U2 - 10.1016/j.jde.2022.12.036

DO - 10.1016/j.jde.2022.12.036

M3 - Article

VL - 352

SP - 153

EP - 188

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -