On multiwell Liouville theorems in higher dimension
Robert L. Jerrard, Andrew Lorent · Advances in Calculus of Variations · 2012
Abstract. We consider certain subsets of the space of matrices of the form and we prove that for , and for connected , there exists a positive constant depending on such that for we have provided u satisfies the inequality . Our main result holds whenever , and generically for in every dimension , as long as the wells satisfy a certain connectivity condition. These conclusions are mostly known when , and they are new for .