TY - JOUR
T1 - Counterexamples related to high-frequency oscillation of Poisson's kernel
AU - Avellaneda, Marco
AU - Lin, Fang Hua
PY - 1987/1
Y1 - 1987/1
N2 - Let {Mathematical expression} where a is a smooth periodic matrix and L0 is the homogenized operator corresponding to the family (Lε). Let D be a nice domain, and let Pε(x, y), P0(x, y) be the Poisson kernels associated with Lε and L0. We show that in general Pε(x, ·) does not converge strongly to P0(x, ·) in Lp, by exhibiting two counterexamples. This result has the following implication in the theory of boundary control of distributed systems: if, with z given, uε(x) = ∫ Pε(x, y)g(y) and u0(x) = ∫P0(x,y)g(y), then, in general,.
AB - Let {Mathematical expression} where a is a smooth periodic matrix and L0 is the homogenized operator corresponding to the family (Lε). Let D be a nice domain, and let Pε(x, y), P0(x, y) be the Poisson kernels associated with Lε and L0. We show that in general Pε(x, ·) does not converge strongly to P0(x, ·) in Lp, by exhibiting two counterexamples. This result has the following implication in the theory of boundary control of distributed systems: if, with z given, uε(x) = ∫ Pε(x, y)g(y) and u0(x) = ∫P0(x,y)g(y), then, in general,.
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U2 - 10.1007/BF01442649
DO - 10.1007/BF01442649
M3 - Article
AN - SCOPUS:34250106154
SN - 0095-4616
VL - 15
SP - 109
EP - 119
JO - Applied Mathematics & Optimization
JF - Applied Mathematics & Optimization
IS - 1
ER -