Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5024670 | Nonlinear Analysis: Theory, Methods & Applications | 2017 | 25 Pages |
Abstract
The aim of this paper is to establish a higher integrability result for very weak solutions of certain parabolic systems whose model is the parabolic p(x,t)-Laplacian system. Under assumptions on the exponent function p:ΩT=ΩÃ(0,T)â(2nn+2,2], it is shown that any very weak solution u:ΩTâRN with |Du|p(â
)(1âε)âL1(ΩT) belongs to the natural energy spaces, i.e. |Du|p(â
)âLloc1(ΩT), provided ε>0 is small enough. This extends the main result of Bögelein and Li (2014) to the subquadratic case.
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Authors
Qifan Li,