Block diagonalization of systems with measurable coefficients
نویسندگان
چکیده
منابع مشابه
Parabolic Equations with Measurable Coefficients
We investigate the unique solvability of second order parabolic equations in non-divergence form in W 1,2 p ((0, T ) × R), p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.
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We prove the unique solvability of second order elliptic equations in non-divergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the martingale problem associated with the elliptic equations.
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We use Bernstein’s technique to show that for any fixed t, strong solutions u(t, x) of the uniformly parabolic equation Lu := aij (t)uxixj−ut = 0 in Q are real analytic in Q(t) = {x : (t, x) ∈ Q}. Here, Q ⊂ Rd+1 is a bounded domain and the coefficients aij(t) are measurable. We also use Bernstein’s technique to obtain interior estimates for pure second derivatives of solutions of the fully nonl...
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Gi j(·, y) = 0 on ∂Ω ∀y ∈ Ω, where δik is the Kronecker delta symbol and δy(·) is the Dirac delta function with a unit mass at y. In the scalar case (i.e., when N = 1), the Green’s matrix becomes a real valued function and is usually called the Green’s function. We prove that if Ω has either finite volume or finite width, then there exists a unique Green’s matrix in Ω; see Theorem 2.12. The sam...
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In this paper we study the effect of block diagonalization of a nearly diagonal matrix by iterating the related Riccati equations. We show that the iteration is fast, if a matrix is diagonally dominant or scaled diagonally dominant and the block partition follows an appropriately defined spectral gap. We also show that both kinds of diagonal dominance are not destroyed after the block diagonali...
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 1994
ISSN: 0716-0917,0717-6279
DOI: 10.22199/s07160917.1994.0001.00002