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$L^{p}$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$

Ralph Chill; Sachi Srivastava — 2008

Bollettino dell'Unione Matematica Italiana

If the second order problem $\ddot{u}+\dot{u}+Au=f$ has $L^{p}$ maximal regularity for some $p\in(1,\infty)$ , then it has $L^{p}$ maximal regularity for every $p\in(1,\infty)$ .

Maximal regularity for second order non-autonomous Cauchy problems

Charles J. K. Batty; Ralph Chill; Sachi Srivastava — 2008

Studia Mathematica

We consider some non-autonomous second order Cauchy problems of the form ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0. We assume that the first order problem u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0, has $L^{p}$ -maximal regularity. Then we establish $L^{p}$ -maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).

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L p Maximal Regularity for Second Order Cauchy Problems is Independent of p

Maximal regularity for second order non-autonomous Cauchy problems

$L^{p}$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$