Lp-estimates for parabolic systems with unbounded coefficients coupled at zero and first order

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:444

Article

Angiuli, Luciana¹  Lorenzi, Luca²  Pallara, Diego^1,3 

[1] Univ Salento, Dipartimento Matemat & Fis Ennio De Giorgi, Via Arnesano, I-73100 Lecce, Italy

[2] Univ Parma, Dipartimento Matemat & Informat, Parco Area Sci 55-A, I-43124 Parma, Italy

[3] Ist Nazl Fis Nucl, Via Arnesano, I-73100 Lecce, Italy

关键词: Parabolic systems;    Unbounded coefficients;    L-p-estimates;    Pointwise gradient estimates;   

DOI  :  10.1016/j.jmaa.2016.06.001

来源: Elsevier

【 摘 要 】

We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space L-p(R-d;R-m) (d, m >= 1) with p is an element of [1, +infinity). Sufficient conditions for the associated evolution operator G(t, s) in C-b(R-d; R-m) to extend to a strongly continuous operator in L-p(R-d; R-m) are given. Some L-p-L-q estimates are also established together with L-p gradient estimates. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free