Abstract
In this article, we present a new kind of fractional derivative D and fractional integral I, which are related to a generalization W s,q(Ω; ∂Ω) of Sobolev-Slobodecki spaces and satisfy a kind of fractional divergence theorem ∫∂Ω(Iv)(y) dS (y) = ∫Ω(Dν)(x) dx for functions ν∈ W s,q(Ω; ∂Ω). Further, we show how this space occurs in a discussion of linear elliptic equations with singular Neumann boundary data.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.