The Conormal Derivative Problem for Equations of Variational Type in Nonsmooth Domains
Gary M. Lieberman · Transactions of the American Mathematical Society · 1992
It is well known that elliptic boundary value problems in smooth domains have smooth solutions, but if the domain is, say, ${C^1}$, the solutions need not be Lipschitz. Recently Korevaar has identified a class of Lipschitz domains, in which solutions of the capillary problem are Lipschitz assuming the contact angle relates correctly to the geometry of the domain. Lipschitz bounds for more general boundary value problems in the same class of domains are proved. Applications to variational inequalities are also considered.