Abstract
This paper is concerned with a special quasilinear elliptic system, which can be seen as a perturbed p-Laplacean, p∈(1,2), in the whole space Rn. For its “shape”, it is close to the p-Stokes system. However, our quasilinear second-order differential operator is given by means of ∇u and not by its symmetric part, so that our system cannot be considered as a p-Stokes system. Hence, it is called modifiedp-Stokes system. We look for the high regularity of the solutions (u,π), in the sense of D2u,∇π∈Lq(Rn),q∈(n,∞). In particular, we get ∇u,π∈C0,α(Rn). As far as we know, such a result of high regularity is the first concerning the coupling of unknowns (u,π). However, our result also holds for the p-Laplacean, and it is the first high regularity result in an unbounded domain.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Nonlinear Analysis: Theory, Methods & Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
