Regularity versus singularities for elliptic problems in two dimensions

الأصل · EN

In two dimensions every weak solution to a nonlinear elliptic system div a(x,u,Du)=0 has Hölder continuous first derivatives provided that standard continuity, ellipticity and growth assumptions hold with a growth exponent p ≥ 2. We give an example showing that this result cannot be extended to the subquadratic case, i.e. that weak solutions are not necessarily continuous if 1< p <2. Furthermore, we discuss related results for variational integrals.