Nonlinear elliptic equations on nonsmooth domains

The Dirichlet problem for strongly nonlinear elliptic equations on a non-Li pschitz domain is studied, It is assumed that the domain is two-dimensional and has a piecewise smooth boundary with a cuspidal point. The global regu larity of a weak solution in fractional-order Sobolev spaces is investigate d. Therefore, a difference quotient technique is applied, which provides re gularity results in Nikolskii spaces. Utilizing the imbedding theorem of Ni kolskii spaces into Sobolev spaces it follows that weak solutions are W-s,W -2(Omega)-functions for all s < 3/2. This result cannot be 2 improved. In f act, there is a counterexample in the case that s = 3/2.