Asymptotic Expansions of Solutions to Δ u–u = f at Infinity

Consider solutions to the equation Δu – u = ƒ in a neighborhood of infinity, B R e = { ( x , y ) : r > R } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003072584/300cbf75-7783-4a6f-9796-7cd4d736d320/content/eq3534.tif"/> , where r is the usual radial polar coordinate. Meyers and Serrin (1960) have studied such exterior problems for linear elliptic partial differential equations. It follows from Theorem 14 of their paper that for ƒ bounded and Hölder continuous, there exists a unique bounded solution satisfying a Dirichlet condition, u a prescribed continuous function on r = R.