"Variational formulas on Lipschitz domains"

A rigorous treatment is given of variational formulas for solutions of certain Dirichlet problems for the Laplace operator on Lipschitz domains. In particular we will extend well-known variational formulas for the torsional rigidity and for capacity from the class of C$^1$domains to the class of Lipschitz domains. A motivation for this work comes from the use of variational methods in the study of Prandtl-Batchelor flows in fluid mechanics.