Maximal regularity of type Lp for abstract parabolic Volterra equations

By Rico Zacher. 2005

120 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0929b4c1fee1e8abb89513f7d616404fb602a787

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In Mathematical Physics

Citations in the corpus

Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients (2008, unknown): “[1], [3], [6], [8], [9], [13], [15], [16].”
Maximal $L^p$-regularity for stochastic evolution equations (2011, background): “ss of I is then deduced from the R-boundedness of J. The estimate 12 JAN VAN NEERVEN, MARK VERAAR, AND LUTZ WEIS (3.10) follows from a combination of (3.7), (3.11), and an interpolation argument (see [88]). Note that (3.11) implies the space-time Ho¨lder regularity estimate kUk Lp(Ω;Cθ− 1 p ([0,∞);D”
Representation of solutions and large-time behavior for fully nonlocal diffusion equations (2015, methodology): “he initial condition of (2.5) for every x∈ Rd. We remark that under appropriate regularity conditions on the data, existence and uniqueness of strong Lp-solutions of (2.5) follows from the results in [45], which are formulated in the framework of abstract parabolic Volterra equations, see also the m”
Strong solutions for a compressible fluid model of Korteweg type (2008, methodology): “For this, we draw on a general trace theorem, which can be found in [17] and [22], reading as follows.”
Fundamental solutions and decay of fully non-local problems (2018, background): “unt of work on such abstract Volterra and integro-diﬀerential equations since the 1970s, in particular on existence and uniqueness, regularity, and long-time behavior of solutions, see, for instance, [8, 15, 34, 35], and the monograph [26]. One of the main objectives of this paper is to prove sharp ”
Traces and embeddings of anisotropic function spaces (2012, unknown): “Stochastic parabolic equations and Volterra integral equations (see [30, 46, 47]) are further scenarios in which intersection spaces, even in an abstract form, come naturally into play.”
Inhomogeneous symbols, the Newton polygon, and maximal Lp-regularity (2008, result): “Actually in [29] this result is proved for J = R+.”
Time fractional diffusion equations: solution concepts, regularity, and long-time behavior (2019, background): “[35, 51].”
Stochastic maximal Lp-regularity (2010, unknown): “surely, and hence, by (5.2) and Theorem 4.3, kA1/2−θS⋄Gk Lp(Ω;Hθ,p(R +;Lq(O))) ≤kC θ(A1/2−θS⋄G)(t)k Lp(R ×Ω;Lq(O)) =k(A1/2−θS θ ⋄G)(t)kLp(R +×Ω;Lq(O)) ≤CkGkLp(R +×Ω;Lq(O;H)). (2) Let θ∈(1 p, 1 2). By [49], Theorem 3.6 (see also [3], Theorem III.4.10.2, and [37], Proposition 3) there is a continuous ”
An $L_q(L_p)$-theory for the time fractional evolution equations with variable coefficients (2015, methodology): “0 > 0, however it is obtained only for the case aij(t,x) = δij with the restrictions α ∈ (0,1) and (1.3). If p = q, an Lp-theory of type (1.1) with the variable coeﬃcients aij(t,x) is presented in [46] under the condition that aij are uniformly continuous in (t,x) and lim |x|→∞ a ij(t,x) exists. ”
Time-fractional diffusion equation in the fractional Sobolev spaces (2015, methodology): “In [28], the maximal regularity of type Lp for the abstract Volterra equations was established by applying the techniques developed in [24].”