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math.CA2019
A Trace Theorem For Sobolev Spaces On The Sierpinski Gasket
Shiping Cao, Shuangping Li, Robert S. Strichartz +1
We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special…
math.CA2019
The Mathieu Differential Equation and Generalizations to Infinite Fractafolds
Shiping Cao, Anthony Coniglio, Xueyan Niu +2
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by c…
math.CA2016
Some Properties of the Derivatives on Sierpinski Gasket Type Fractals
Shiping Cao, Hua Qiu
In this paper, we focus on Strichartz's derivatives, a family of derivatives including the normal derivative, on p.c.f. (post critically finite) fractals, which are defined at vert…