Abstract
This article is concerned with an obstacle problem for nonlinear subelliptic systems of second order with VMO coefficients. It is shown, based on a modification of A-harmonic approximation argument, that the gradient of weak solution to the corresponding obstacle problem belongs to the Morrey space L_{X,mathrm{loc}}^{2,lambda }.
Highlights
The function u ∈ Kθψ is called a weak solution to the obstacle problem related to (1.1) if
An important step of this kind of methods is to establish the higher integrability of gradients of weak solutions. These arguments were used to prove the Morrey regularity and Hölder continuity for weak solutions to the obstacle problems associated with a single elliptic equation with constant coefficients or continuous coefficients; see [18,19,20,21,22]
In the present paper we study the interior regularity of weak solutions to the obstacle problem related to the system (1.1) by the technique of A-harmonic approximation, which implies that these solutions have the same kind of regularity as the weak solutions of (1.1)
Summary
The function u ∈ Kθψ is called a weak solution to the obstacle problem related to (1.1) if In [2,3,4], Campanato obtained the L2,λ-regularity and Hölder continuity for the weak solutions of elliptic systems with continuous coefficients. Huang in [9] established the gradient estimates in the generalized Morrey spaces of weak solutions to the linear elliptic systems with VMO coefficients.
Sign-in/Register to view highlights & summary 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 callDisclaimer: 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.
