Suppose [epsilon] [is a member of the set] [0, 1) and let theta [subscipt epsilon] (t) = (1 − [epsilon]) [square root of] (2tln [subscript] 2 t). Let L [to the power of epsilon] [subscript] t denote the amount of local time spent by Brownian motion on the curve [theta subscript epsilon] (s) before time t. If [epsilon] > 0 ...

We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum is greater than 0, and some other families of domains where it is equal to 0. We also give a new result on "trap domains" defined in [BCM], i.e., domains where reflecting ...