Dirichlet boundary data with singularities^†

^†Research supported by the N.S.E.R.C. Of Canada under grant A9097

Abstract

This paper studies the effect of singularities of boundary data on the smoothness of solutions of the Dirichlet problem for second order linear elliptic equations in two variables with smooth coefficients in a domain with smooth boundary. It is shown that these solutions are Holder continuous in the closure of the domain, but are not of class C¹

^†Research supported by the N.S.E.R.C. Of Canada under grant A9097

^†Research supported by the N.S.E.R.C. Of Canada under grant A9097

Notes

^†Research supported by the N.S.E.R.C. Of Canada under grant A9097