An Elementary Boundary Value Problem
نویسنده
چکیده
IT is intuitively obvious that if a simple continuous curve is given in the (x, 2/)-plane, and a continuous distribution of values along the curve, there will exist functions of x and y which are continuous in both variables together, and which take on the prescribed values along the curve. It is the purpose of the present note to give an analytic proof of this fact, by elementary means, and, in particular, without reference to potential theory.* The problem will be treated first for the case of a rectifiable curve, then for an arbitrary Jordan curve. Let the equations
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