Variational formulas on Lipschitz domains
Alan R. Elcrat, Kenneth G. Miller · Transactions of the American Mathematical Society · 1995
A rigorous treatment is given of variational formulas for solutions of certain Dirichlet problems for the Laplace operator on Lipschitz domains under interior variations. In particular we extend well-known variational formulas for the torsional rigidity and for capacity from the class of C 1 {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.