We find a sufficient condition guaranteeing well-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W1,1(Ω; Rm) with boundary datum equal to zero. We remark that this condition does not involve global convexity of the integrand and therefore it allows us to find well-posedness properties of two classes of nonconvex problems recently studied: functionals depending only on the gradient and radially symmetric functionals.
展开▼
机译：我们找到了一个充分条件，可以保证在Sobolev空间W 1,1 （Ω; R m ）上的多重积分最小化的强烈意义上保证适定性基准等于零。我们注意到，该条件不涉及被积体的全局凸性，因此它使我们能够找到最近研究的两类非凸问题的适定性：仅取决于梯度的函数和径向对称泛函。
展开▼
