A uniform trace theorem for Dirichlet forms on Sierpinski fractals

Abstract

We establish trace theorems for the self-similar Dirichlet forms on the Sierpinski gasket and the Sierpinski carpet to their subsets generated by cutting with a straight line. For the Sierpinski gasket, the straight line can be in any direction. For the Sierpinski carpet, we require the straight line parallel to an edge of the carpet. The trace forms are expressed in term of values of functions along the cut, in a uniform way independent of the choices of the line.