Dirichlet Problem with L1(S) Boundary Values

Let D be a connected bounded domain in R2, S its boundary, which is closed and C2-smooth. Consider the Dirichlet problem Δu=0inD,u|S=h, where h∈L1(S). The aim of this paper to prove that above has solution for an arbitrary h∈L1(S), unique. result new. method proof definition L1(S)-boundary value harmonic function given. No embedding theorems are used. history goes back 1828. is, author’s knowledge, first 194 years research (since 1828) yields existence uniqueness with boundary values L1(S).