Butterfly support for o diagonal coeficients and boundedness of solutions to quasilinear elliptic systems

We consider quasilinear elliptic systems in divergence form. In general,we cannot expect thatweak solutions are locally bounded because of De Giorgi’s counterexample. Here we assume that off-diagonal coeficients have a "butterfly support": this allows us to prove local boundedness of weak solutions.publishe

On the H\uf6lder continuity for a class of vectorial problems

In this paper we prove local H\uf6lder continuity of vectorial local minimizers of special classes of integral functionals with rank-one and polyconvex integrands. The energy densities satisfy suitable structure assumptions and may have neither radial nor quasi-diagonal structure. The regularity of minimizers is obtained by proving that each component stays in a suitable De Giorgi class and, from this, we conclude about the H\uf6lder continuity. In the final section, we provide some non-trivial applications of our results

A Boundedness Result for Minimizers of Some Polyconvex Integrals

We consider polyconvex functionals of the Calculus of Variations defined on maps from the three-dimensional Euclidean space into itself. Counterexamples show that minimizers need not to be bounded. We find conditions on the structure of the functional, which force minimizers to be locally bounded