The mixed problem for the Laplacian in Lipschitz domains

We consider the mixed boundary value problem or Zaremba's problem for the Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We assume that the boundary between the sets where we specify Dirichlet and Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p and the Dirichlet data is in the Sobolev space of functions having one derivative in L^p for some p near 1. Under these conditions, there is a unique solution to the mixed problem with the non-tangential maximal function of the gradient of the solution in L^p of the boundary. We also obtain results with data from Hardy spaces when p=1.Comment: Version 5 includes a correction to one step of the main proof. Since the paper appeared long ago, this submission includes the complete paper, followed by a short section that gives the correction to one step in the proo

Management of intra-abdominal infections : recommendations by the WSES 2016 consensus conference

This paper reports on the consensus conference on the management of intra-abdominal infections (IAIs) which was held on July 23, 2016, in Dublin, Ireland, as a part of the annual World Society of Emergency Surgery (WSES) meeting. This document covers all aspects of the management of IAIs. The Grading of Recommendations Assessment, Development and Evaluation recommendation is used, and this document represents the executive summary of the consensus conference findings.Peer reviewe